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Benford's Law and Sequences: Shiny app at http://www.statistics.calpoly.edu/shiny
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| Benford's Law with Sequences Shiny App | |
| Base R code created by Jimmy Doi | |
| Shiny app files created by Jimmy Doi | |
| Cal Poly Statistics Dept Shiny Series | |
| http://statistics.calpoly.edu/shiny |
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| Title: Benford's Law and Sequences | |
| Author: Jimmy Doi | |
| AuthorUrl: http://www.calpoly.edu/~jdoi | |
| License: MIT | |
| DisplayMode: Normal | |
| Tags: Benford's Law, Sequences | |
| Type: Shiny |
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| The MIT License (MIT) | |
| Copyright (c) 2015 Jimmy Doi | |
| Permission is hereby granted, free of charge, to any person obtaining a copy | |
| of this software and associated documentation files (the "Software"), to deal | |
| in the Software without restriction, including without limitation the rights | |
| to use, copy, modify, merge, publish, distribute, sublicense, and/or sell | |
| copies of the Software, and to permit persons to whom the Software is | |
| furnished to do so, subject to the following conditions: | |
| The above copyright notice and this permission notice shall be included in | |
| all copies or substantial portions of the Software. | |
| THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR | |
| IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, | |
| FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE | |
| AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER | |
| LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, | |
| OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN | |
| THE SOFTWARE. |
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| # ---------------------------------------- | |
| # App Title: Benford's Law and Sequences | |
| # Author: Jimmy Doi | |
| # ---------------------------------------- | |
| library(RColorBrewer) | |
| library(shinyIncubator) | |
| ######################################## | |
| seq.gen <- function(length,val.1,val.2){ | |
| seq <- numeric(length) | |
| seq[1] <- val.1 | |
| seq[2] <- val.2 | |
| for (i in 3:length) { | |
| seq[i] <- seq[i-1]+seq[i-2] | |
| } | |
| return(seq) | |
| } | |
| ######################################## | |
| pow.gen <- function(base,length){ | |
| seq <- base**(1:length) | |
| return(seq) | |
| } | |
| ######################################## | |
| prime.gen <- function(n){ | |
| n <- as.integer(n) | |
| if(n > 1e8) stop("n too large") | |
| primes <- rep(TRUE, n) | |
| primes[1] <- FALSE | |
| last.prime <- 2L | |
| fsqr <- floor(sqrt(n)) | |
| while (last.prime <= fsqr) | |
| { | |
| primes[seq.int(2L*last.prime, n, last.prime)] <- FALSE | |
| sel <- which(primes[(last.prime+1):(fsqr+1)]) | |
| if(any(sel)){ | |
| last.prime <- last.prime + min(sel) | |
| }else last.prime <- fsqr+1 | |
| } | |
| which(primes) | |
| } | |
| ######################################## | |
| string.1st <- function(sequence,max){ | |
| string1 <- substr(as.character(sequence[1:max]),1,1) | |
| # string1<-paste(" ",string1,sep="") | |
| return(string1) | |
| } | |
| ######################################## | |
| string.2nd <- function(sequence,max){ | |
| string2 <- substr(as.character(sequence[1:max]),2,1000000L) | |
| string2.a<-paste(string2,", ",sep="") | |
| string2.a[max]<-string2[max] | |
| return(string2.a) | |
| } | |
| ######################################## | |
| print.string <- function(string,num){ | |
| #names(string)<-"" | |
| return(string[num]) | |
| } | |
| ######################################## | |
| goodness.test <- function(sequence){ | |
| string <- substr(as.character(sequence),1,1) | |
| first.digits <- as.integer(string) | |
| # In the event any of the 9 possible digits is not observed in the string, | |
| # table(first.digits) will not display all digits 1, 2, ..., 9. An example is | |
| # | |
| # NAME 1 2 3 4 5 6 7 9 | |
| # FREQ 12 11 9 8 6 5 4 2 | |
| # | |
| # Here, obs <- as.integer(table(first.digits)) would only contain 8 elements. | |
| # To correct for this, initialize obs to a zero vector, loop through NAME, | |
| # find FREQ corresponding to NAME,then paste that FREQ in obs[NAME]. | |
| # This will also work for the case when all 9 possible digits are observed. | |
| Obs <- seq(0,0,,9) | |
| for (i in as.numeric(names(table(first.digits)))) { | |
| pos <- which(as.numeric(names(table(first.digits)))==i) | |
| Obs[i]<- as.numeric(table(first.digits))[pos] | |
| } | |
| i <- seq(1,9) | |
| Exp <- length(sequence)*log10(1+1/i) | |
| Digit <- seq(1,9) | |
| #print(info) | |
| chisq <- sum(((Obs-Exp)**2)/Exp) | |
| Exp <- round(Exp,3) | |
| info <- cbind(Digit,Obs,Exp) | |
| rownames(info)<-rep("",nrow(info)) | |
| #print(chisq) | |
| p.value <- 1-pchisq(chisq,8) | |
| text.chi <- paste("Chi Square = ",format(round(chisq,3),nsmall=3),sep="") | |
| names(text.chi)<-"" | |
| text.pval <- paste("P Value = ",format(round(p.value,3),nsmall=3),sep="") | |
| names(text.pval)<-"" | |
| print(info) | |
| print(text.chi,quote=F) | |
| print(text.pval,quote=F) | |
| } | |
| ######################################## | |
| pr.goodness.test <- function(sequence,big.n){ | |
| string <- substr(as.character(sequence),1,1) | |
| first.digits <- as.integer(string) | |
| # In the event any of the 9 possible digits is not observed in the string, | |
| # table(first.digits) will not display all digits 1, 2, ..., 9. An example is | |
| # | |
| # NAME 1 2 3 4 5 6 7 9 | |
| # FREQ 12 11 9 8 6 5 4 2 | |
| # | |
| # Here, obs <- as.integer(table(first.digits)) would only contain 8 elements. | |
| # To correct for this, initialize obs to a zero vector, loop through NAME, | |
| # find FREQ corresponding to NAME,then paste that FREQ in obs[NAME]. | |
| # This will also work for the case when all 9 possible digits are observed. | |
| Obs <- seq(0,0,,9) | |
| for (i in as.numeric(names(table(first.digits)))) { | |
| pos <- which(as.numeric(names(table(first.digits)))==i) | |
| Obs[i]<- as.numeric(table(first.digits))[pos] | |
| } | |
| i <- seq(1,9) | |
| alpha <- 1/(log(big.n)-1.10) | |
| gbl <- 1/(10**(1-alpha)-1)*((i+1)**(1-alpha)-i**(1-alpha)) | |
| Exp <- length(sequence)*gbl | |
| Digit <- seq(1,9) | |
| chisq <- sum(((Obs-Exp)**2)/Exp) | |
| Exp <- round(Exp,3) | |
| info <- cbind(Digit,Obs,Exp) | |
| rownames(info)<-rep("",nrow(info)) | |
| p.value <- 1-pchisq(chisq,8) | |
| text.chi <- paste("Chi Square = ",format(round(chisq,3),nsmall=3),sep="") | |
| names(text.chi)<-"" | |
| text.pval <- paste("P Value = ",format(round(p.value,3),nsmall=3),sep="") | |
| names(text.pval)<-"" | |
| print(info) | |
| print(text.chi,quote=F) | |
| print(text.pval,quote=F) | |
| } | |
| ############################################ | |
| pmf.compare<-function(sequence){ | |
| string <- substr(as.character(sequence),1,1) | |
| first.digits <- as.integer(string) | |
| # In the event any of the 9 possible digits is not observed in the string, | |
| # table(first.digits) will not display all digits 1, 2, ..., 9. An example is | |
| # | |
| # NAME 1 2 3 4 5 6 7 9 | |
| # FREQ 12 11 9 8 6 5 4 2 | |
| # | |
| # Here, obs <- as.integer(table(first.digits)) would only contain 8 elements. | |
| # To correct for this, initialize obs to a zero vector, loop through NAME, | |
| # find FREQ corresponding to NAME,then paste that FREQ in obs[NAME]. | |
| # This will also work for the case when all 9 possible digits are observed. | |
| Obs <- seq(0,0,,9) | |
| for (i in as.numeric(names(table(first.digits)))) { | |
| pos <- which(as.numeric(names(table(first.digits)))==i) | |
| Obs[i]<- as.numeric(table(first.digits))[pos] | |
| } | |
| i <- seq(1,9) | |
| pmf.Exp <- cbind(seq(1,9)+0.065,log10(1+1/i)) | |
| pmf.Obs <- cbind(seq(1,9)-0.065,Obs/sum(Obs)) | |
| col1 <- brewer.pal(n = 12, name = "Paired")[8] | |
| col2 <- brewer.pal(n = 12, name = "Paired")[2] | |
| par(mar=c(3.5,4.5,2,0)) | |
| my.lwd <- 3.75 | |
| if (max(pmf.Obs[,2])>=max(pmf.Exp[,2])){ | |
| plot(pmf.Obs[,1],pmf.Obs[,2],type="n",col=col1,xlim=c(0.75,9.25), xlab="",ylab="Proportion", xaxt="n", main="Proportion of First Digits") | |
| axis(1, at=seq(1,9), labels=c("1","2","3","4","5","6","7","8","9")) | |
| mtext("First Digit",1,line=2.5) | |
| for (i in 1:nrow(pmf.Obs)){ | |
| lines(c(pmf.Obs[i,1],pmf.Obs[i,1]),c(0,pmf.Obs[i,2]),col=col1,lwd=my.lwd) | |
| } | |
| for (i in 1:nrow(pmf.Exp)){ | |
| lines(c(pmf.Exp[i,1],pmf.Exp[i,1]),c(0,pmf.Exp[i,2]),col=col2,lwd=my.lwd) | |
| legend("topright", inset=.02, | |
| c("Observed Proportion","Benford's Law"), fill=c(col1,col2), horiz=F) | |
| } | |
| } | |
| if (max(pmf.Obs[,2])<max(pmf.Exp[,2])){ | |
| plot(pmf.Exp[,1],pmf.Exp[,2],type="n",col=col2,xlim=c(0.75,9.25), xlab="", ylab="Proportion", xaxt="n", main="Proportion of First Digits") | |
| axis(1, at=seq(1,9), labels=c("1","2","3","4","5","6","7","8","9")) | |
| mtext("First Digit",1,line=2.5) | |
| for (i in 1:nrow(pmf.Obs)){ | |
| lines(c(pmf.Exp[i,1],pmf.Exp[i,1]),c(0,pmf.Exp[i,2]),col=col2,lwd=my.lwd) | |
| } | |
| for (i in 1:nrow(pmf.Obs)){ | |
| lines(c(pmf.Obs[i,1],pmf.Obs[i,1]),c(0,pmf.Obs[i,2]),col=col1,lwd=my.lwd) | |
| } | |
| legend("topright", inset=.02, | |
| c("Observed Proportion","Benford's Law"), fill=c(col1,col2), horiz=F) | |
| } | |
| } | |
| ############################################ | |
| pr.pmf.compare<-function(sequence,big.n){ | |
| string <- substr(as.character(sequence),1,1) | |
| first.digits <- as.integer(string) | |
| # In the event any of the 9 possible digits is not observed in the string, | |
| # table(first.digits) will not display all digits 1, 2, ..., 9. An example is | |
| # | |
| # NAME 1 2 3 4 5 6 7 9 | |
| # FREQ 12 11 9 8 6 5 4 2 | |
| # | |
| # Here, obs <- as.integer(table(first.digits)) would only contain 8 elements. | |
| # To correct for this, initialize obs to a zero vector, loop through NAME, | |
| # find FREQ corresponding to NAME,then paste that FREQ in obs[NAME]. | |
| # This will also work for the case when all 9 possible digits are observed. | |
| Obs <- seq(0,0,,9) | |
| for (i in as.numeric(names(table(first.digits)))) { | |
| pos <- which(as.numeric(names(table(first.digits)))==i) | |
| Obs[i]<- as.numeric(table(first.digits))[pos] | |
| } | |
| i <- seq(1,9) | |
| alpha <- 1/(log(big.n)-1.10) | |
| gbl <- 1/(10**(1-alpha)-1)*((i+1)**(1-alpha)-i**(1-alpha)) | |
| pmf.Exp <- cbind(seq(1,9)+0.065,gbl) | |
| pmf.Obs <- cbind(seq(1,9)-0.065,Obs/sum(Obs)) | |
| col1 <- brewer.pal(n = 12, name = "Paired")[8] | |
| col2 <- brewer.pal(n = 12, name = "Paired")[2] | |
| par(mar=c(3.5,4.5,2,0)) | |
| my.lwd <- 3.75 | |
| if (max(pmf.Obs[,2])>=max(pmf.Exp[,2])){ | |
| plot(pmf.Obs[,1],pmf.Obs[,2],type="n",col=col1,xlim=c(0.75,9.25), xlab="",ylab="Proportion", xaxt="n", main="Proportion of First Digits", | |
| ylim=c(0.06, | |
| max(1.05*max(pmf.Obs[,2]),1.05*max(pmf.Exp[,2]))) | |
| ) | |
| axis(1, at=seq(1,9), labels=c("1","2","3","4","5","6","7","8","9")) | |
| mtext("First Digit",1,line=2.5) | |
| for (i in 1:nrow(pmf.Obs)){ | |
| lines(c(pmf.Obs[i,1],pmf.Obs[i,1]),c(0,pmf.Obs[i,2]),col=col1,lwd=my.lwd) | |
| } | |
| for (i in 1:nrow(pmf.Exp)){ | |
| lines(c(pmf.Exp[i,1],pmf.Exp[i,1]),c(0,pmf.Exp[i,2]),col=col2,lwd=my.lwd) | |
| legend("topright", inset=.02, | |
| c("Observed Proportion","Generalized Benford's Law"), fill=c(col1,col2), horiz=F) | |
| } | |
| } | |
| if (max(pmf.Obs[,2])<max(pmf.Exp[,2])){ | |
| plot(pmf.Exp[,1],pmf.Exp[,2],type="n",col=col2,xlim=c(0.75,9.25), xlab="", ylab="Proportion", xaxt="n", main="Proportion of First Digits", | |
| ylim=c(0.06, | |
| max(1.05*max(pmf.Obs[,2]),1.05*max(pmf.Exp[,2])))) | |
| axis(1, at=seq(1,9), labels=c("1","2","3","4","5","6","7","8","9")) | |
| mtext("First Digit",1,line=2.5) | |
| for (i in 1:nrow(pmf.Obs)){ | |
| lines(c(pmf.Exp[i,1],pmf.Exp[i,1]),c(0,pmf.Exp[i,2]),col=col2,lwd=my.lwd) | |
| } | |
| for (i in 1:nrow(pmf.Obs)){ | |
| lines(c(pmf.Obs[i,1],pmf.Obs[i,1]),c(0,pmf.Obs[i,2]),col=col1,lwd=my.lwd) | |
| } | |
| legend("topright", inset=.02, | |
| c("Observed Proportion","Generalized Benford's Law"), fill=c(col1,col2), horiz=F) | |
| } | |
| } | |
| ############################################################################## | |
| # Shiny Server Contents | |
| ############################################################################## | |
| shinyServer(function(input, output, session) { | |
| ######################################################################### | |
| ## Additive Sequence | |
| ######################################################################### | |
| withProgress(session, { | |
| setProgress(message = "Calculating, please wait.", | |
| detail = " ", value=1) | |
| output$val.1st <- renderText({input$seq1}) | |
| output$val.2nd <- renderText({input$seq2}) | |
| output$textlength <- renderText({input$length}) | |
| seqInput <- reactive({ | |
| seq.gen(input$length,input$seq1,input$seq2) | |
| }) | |
| output$goodness <- renderPrint({ | |
| goodness.test(seqInput()) | |
| }) | |
| firstDigit <- reactive({ | |
| string.1st(seqInput(),50) | |
| }) | |
| restDigit <- reactive({ | |
| string.2nd(seqInput(),50) | |
| }) | |
| output$num.1a <- renderText({print.string(firstDigit(), 1)}) | |
| output$num.1b <- renderText({print.string(restDigit(), 1)}) | |
| output$num.2a <- renderText({print.string(firstDigit(), 2)}) | |
| output$num.2b <- renderText({print.string(restDigit(), 2)}) | |
| output$num.3a <- renderText({print.string(firstDigit(), 3)}) | |
| output$num.3b <- renderText({print.string(restDigit(), 3)}) | |
| output$num.4a <- renderText({print.string(firstDigit(), 4)}) | |
| output$num.4b <- renderText({print.string(restDigit(), 4)}) | |
| output$num.5a <- renderText({print.string(firstDigit(), 5)}) | |
| output$num.5b <- renderText({print.string(restDigit(), 5)}) | |
| output$num.6a <- renderText({print.string(firstDigit(), 6)}) | |
| output$num.6b <- renderText({print.string(restDigit(), 6)}) | |
| output$num.7a <- renderText({print.string(firstDigit(), 7)}) | |
| output$num.7b <- renderText({print.string(restDigit(), 7)}) | |
| output$num.8a <- renderText({print.string(firstDigit(), 8)}) | |
| output$num.8b <- renderText({print.string(restDigit(), 8)}) | |
| output$num.9a <- renderText({print.string(firstDigit(), 9)}) | |
| output$num.9b <- renderText({print.string(restDigit(), 9)}) | |
| output$num.10a <- renderText({print.string(firstDigit(),10)}) | |
| output$num.10b <- renderText({print.string(restDigit(), 10)}) | |
| output$num.11a <- renderText({print.string(firstDigit(),11)}) | |
| output$num.11b <- renderText({print.string(restDigit(), 11)}) | |
| output$num.12a <- renderText({print.string(firstDigit(),12)}) | |
| output$num.12b <- renderText({print.string(restDigit(), 12)}) | |
| output$num.13a <- renderText({print.string(firstDigit(),13)}) | |
| output$num.13b <- renderText({print.string(restDigit(), 13)}) | |
| output$num.14a <- renderText({print.string(firstDigit(),14)}) | |
| output$num.14b <- renderText({print.string(restDigit(), 14)}) | |
| output$num.15a <- renderText({print.string(firstDigit(),15)}) | |
| output$num.15b <- renderText({print.string(restDigit(), 15)}) | |
| output$num.16a <- renderText({print.string(firstDigit(),16)}) | |
| output$num.16b <- renderText({print.string(restDigit(), 16)}) | |
| output$num.17a <- renderText({print.string(firstDigit(),17)}) | |
| output$num.17b <- renderText({print.string(restDigit(), 17)}) | |
| output$num.18a <- renderText({print.string(firstDigit(),18)}) | |
| output$num.18b <- renderText({print.string(restDigit(), 18)}) | |
| output$num.19a <- renderText({print.string(firstDigit(),19)}) | |
| output$num.19b <- renderText({print.string(restDigit(), 19)}) | |
| output$num.20a <- renderText({print.string(firstDigit(),20)}) | |
| output$num.20b <- renderText({print.string(restDigit(), 20)}) | |
| output$num.21a <- renderText({print.string(firstDigit(), 21)}) | |
| output$num.21b <- renderText({print.string(restDigit(), 21)}) | |
| output$num.22a <- renderText({print.string(firstDigit(), 22)}) | |
| output$num.22b <- renderText({print.string(restDigit(), 22)}) | |
| output$num.23a <- renderText({print.string(firstDigit(), 23)}) | |
| output$num.23b <- renderText({print.string(restDigit(), 23)}) | |
| output$num.24a <- renderText({print.string(firstDigit(), 24)}) | |
| output$num.24b <- renderText({print.string(restDigit(), 24)}) | |
| output$num.25a <- renderText({print.string(firstDigit(), 25)}) | |
| output$num.25b <- renderText({print.string(restDigit(), 25)}) | |
| output$num.26a <- renderText({print.string(firstDigit(), 26)}) | |
| output$num.26b <- renderText({print.string(restDigit(), 26)}) | |
| output$num.27a <- renderText({print.string(firstDigit(), 27)}) | |
| output$num.27b <- renderText({print.string(restDigit(), 27)}) | |
| output$num.28a <- renderText({print.string(firstDigit(), 28)}) | |
| output$num.28b <- renderText({print.string(restDigit(), 28)}) | |
| output$num.29a <- renderText({print.string(firstDigit(), 29)}) | |
| output$num.29b <- renderText({print.string(restDigit(), 29)}) | |
| output$num.30a <- renderText({print.string(firstDigit(),30)}) | |
| output$num.30b <- renderText({print.string(restDigit(), 30)}) | |
| output$num.31a <- renderText({print.string(firstDigit(), 31)}) | |
| output$num.31b <- renderText({print.string(restDigit(), 31)}) | |
| output$num.32a <- renderText({print.string(firstDigit(), 32)}) | |
| output$num.32b <- renderText({print.string(restDigit(), 32)}) | |
| output$num.33a <- renderText({print.string(firstDigit(), 33)}) | |
| output$num.33b <- renderText({print.string(restDigit(), 33)}) | |
| output$num.34a <- renderText({print.string(firstDigit(), 34)}) | |
| output$num.34b <- renderText({print.string(restDigit(), 34)}) | |
| output$num.35a <- renderText({print.string(firstDigit(), 35)}) | |
| output$num.35b <- renderText({print.string(restDigit(), 35)}) | |
| output$num.36a <- renderText({print.string(firstDigit(), 36)}) | |
| output$num.36b <- renderText({print.string(restDigit(), 36)}) | |
| output$num.37a <- renderText({print.string(firstDigit(), 37)}) | |
| output$num.37b <- renderText({print.string(restDigit(), 37)}) | |
| output$num.38a <- renderText({print.string(firstDigit(), 38)}) | |
| output$num.38b <- renderText({print.string(restDigit(), 38)}) | |
| output$num.39a <- renderText({print.string(firstDigit(), 39)}) | |
| output$num.39b <- renderText({print.string(restDigit(), 39)}) | |
| output$num.40a <- renderText({print.string(firstDigit(),40)}) | |
| output$num.40b <- renderText({print.string(restDigit(), 40)}) | |
| output$num.41a <- renderText({print.string(firstDigit(), 41)}) | |
| output$num.41b <- renderText({print.string(restDigit(), 41)}) | |
| output$num.42a <- renderText({print.string(firstDigit(), 42)}) | |
| output$num.42b <- renderText({print.string(restDigit(), 42)}) | |
| output$num.43a <- renderText({print.string(firstDigit(), 43)}) | |
| output$num.43b <- renderText({print.string(restDigit(), 43)}) | |
| output$num.44a <- renderText({print.string(firstDigit(), 44)}) | |
| output$num.44b <- renderText({print.string(restDigit(), 44)}) | |
| output$num.45a <- renderText({print.string(firstDigit(), 45)}) | |
| output$num.45b <- renderText({print.string(restDigit(), 45)}) | |
| output$num.46a <- renderText({print.string(firstDigit(), 46)}) | |
| output$num.46b <- renderText({print.string(restDigit(), 46)}) | |
| output$num.47a <- renderText({print.string(firstDigit(), 47)}) | |
| output$num.47b <- renderText({print.string(restDigit(), 47)}) | |
| output$num.48a <- renderText({print.string(firstDigit(), 48)}) | |
| output$num.48b <- renderText({print.string(restDigit(), 48)}) | |
| output$num.49a <- renderText({print.string(firstDigit(), 49)}) | |
| output$num.49b <- renderText({print.string(restDigit(), 49)}) | |
| output$num.50a <- renderText({print.string(firstDigit(),50)}) | |
| output$num.50b <- renderText({print.string(restDigit(), 50)}) | |
| output$pmf <- renderPlot({ | |
| pmf.compare(seqInput()) | |
| }) | |
| ####################################################################################### | |
| output$powlength <- renderText({input$pow.length}) | |
| e.seqInput <- reactive({ | |
| pow.gen(input$pow.base,input$pow.length) | |
| }) | |
| output$e.goodness <- renderPrint({ | |
| goodness.test(e.seqInput()) | |
| }) | |
| e.firstDigit <- reactive({ | |
| string.1st(e.seqInput(),20) | |
| }) | |
| e.restDigit <- reactive({ | |
| string.2nd(e.seqInput(),20) | |
| }) | |
| output$e.num.1a <- renderText({print.string(e.firstDigit(), 1)}) | |
| output$e.num.1b <- renderText({print.string(e.restDigit(), 1)}) | |
| output$e.num.2a <- renderText({print.string(e.firstDigit(), 2)}) | |
| output$e.num.2b <- renderText({print.string(e.restDigit(), 2)}) | |
| output$e.num.3a <- renderText({print.string(e.firstDigit(), 3)}) | |
| output$e.num.3b <- renderText({print.string(e.restDigit(), 3)}) | |
| output$e.num.4a <- renderText({print.string(e.firstDigit(), 4)}) | |
| output$e.num.4b <- renderText({print.string(e.restDigit(), 4)}) | |
| output$e.num.5a <- renderText({print.string(e.firstDigit(), 5)}) | |
| output$e.num.5b <- renderText({print.string(e.restDigit(), 5)}) | |
| output$e.num.6a <- renderText({print.string(e.firstDigit(), 6)}) | |
| output$e.num.6b <- renderText({print.string(e.restDigit(), 6)}) | |
| output$e.num.7a <- renderText({print.string(e.firstDigit(), 7)}) | |
| output$e.num.7b <- renderText({print.string(e.restDigit(), 7)}) | |
| output$e.num.8a <- renderText({print.string(e.firstDigit(), 8)}) | |
| output$e.num.8b <- renderText({print.string(e.restDigit(), 8)}) | |
| output$e.num.9a <- renderText({print.string(e.firstDigit(), 9)}) | |
| output$e.num.9b <- renderText({print.string(e.restDigit(), 9)}) | |
| output$e.num.10a <- renderText({print.string(e.firstDigit(),10)}) | |
| output$e.num.10b <- renderText({print.string(e.restDigit(), 10)}) | |
| output$e.num.11a <- renderText({print.string(e.firstDigit(),11)}) | |
| output$e.num.11b <- renderText({print.string(e.restDigit(), 11)}) | |
| output$e.num.12a <- renderText({print.string(e.firstDigit(),12)}) | |
| output$e.num.12b <- renderText({print.string(e.restDigit(), 12)}) | |
| output$e.num.13a <- renderText({print.string(e.firstDigit(),13)}) | |
| output$e.num.13b <- renderText({print.string(e.restDigit(), 13)}) | |
| output$e.num.14a <- renderText({print.string(e.firstDigit(),14)}) | |
| output$e.num.14b <- renderText({print.string(e.restDigit(), 14)}) | |
| output$e.num.15a <- renderText({print.string(e.firstDigit(),15)}) | |
| output$e.num.15b <- renderText({print.string(e.restDigit(), 15)}) | |
| output$e.num.16a <- renderText({print.string(e.firstDigit(),16)}) | |
| output$e.num.16b <- renderText({print.string(e.restDigit(), 16)}) | |
| output$e.num.17a <- renderText({print.string(e.firstDigit(),17)}) | |
| output$e.num.17b <- renderText({print.string(e.restDigit(), 17)}) | |
| output$e.num.18a <- renderText({print.string(e.firstDigit(),18)}) | |
| output$e.num.18b <- renderText({print.string(e.restDigit(), 18)}) | |
| output$e.num.19a <- renderText({print.string(e.firstDigit(),19)}) | |
| output$e.num.19b <- renderText({print.string(e.restDigit(), 19)}) | |
| output$e.num.20a <- renderText({print.string(e.firstDigit(),20)}) | |
| output$e.num.20b <- renderText({print.string(e.restDigit(), 20)}) | |
| output$e.pmf <- renderPlot({pmf.compare(e.seqInput())}) | |
| ######################################################################### | |
| ## Power Sequence | |
| ######################################################################### | |
| pr.seqInput <- reactive({ | |
| pr.big.n <-as.integer(input$my.n) | |
| prime.gen(pr.big.n) | |
| }) | |
| output$num.primes <- reactive({length(pr.seqInput())}) | |
| output$pr.goodness <- renderPrint({ | |
| pr.big.n <-as.integer(input$my.n) | |
| pr.goodness.test(pr.seqInput(),pr.big.n) | |
| }) | |
| pr.firstDigit <- reactive({ | |
| string.1st(pr.seqInput(),80) | |
| }) | |
| pr.restDigit <- reactive({ | |
| string.2nd(pr.seqInput(),80) | |
| }) | |
| output$pr.num.1a <- renderText({print.string(pr.firstDigit(), 1)}) | |
| output$pr.num.1b <- renderText({print.string(pr.restDigit(), 1)}) | |
| output$pr.num.2a <- renderText({print.string(pr.firstDigit(), 2)}) | |
| output$pr.num.2b <- renderText({print.string(pr.restDigit(), 2)}) | |
| output$pr.num.3a <- renderText({print.string(pr.firstDigit(), 3)}) | |
| output$pr.num.3b <- renderText({print.string(pr.restDigit(), 3)}) | |
| output$pr.num.4a <- renderText({print.string(pr.firstDigit(), 4)}) | |
| output$pr.num.4b <- renderText({print.string(pr.restDigit(), 4)}) | |
| output$pr.num.5a <- renderText({print.string(pr.firstDigit(), 5)}) | |
| output$pr.num.5b <- renderText({print.string(pr.restDigit(), 5)}) | |
| output$pr.num.6a <- renderText({print.string(pr.firstDigit(), 6)}) | |
| output$pr.num.6b <- renderText({print.string(pr.restDigit(), 6)}) | |
| output$pr.num.7a <- renderText({print.string(pr.firstDigit(), 7)}) | |
| output$pr.num.7b <- renderText({print.string(pr.restDigit(), 7)}) | |
| output$pr.num.8a <- renderText({print.string(pr.firstDigit(), 8)}) | |
| output$pr.num.8b <- renderText({print.string(pr.restDigit(), 8)}) | |
| output$pr.num.9a <- renderText({print.string(pr.firstDigit(), 9)}) | |
| output$pr.num.9b <- renderText({print.string(pr.restDigit(), 9)}) | |
| output$pr.num.10a <- renderText({print.string(pr.firstDigit(),10)}) | |
| output$pr.num.10b <- renderText({print.string(pr.restDigit(), 10)}) | |
| output$pr.num.11a <- renderText({print.string(pr.firstDigit(),11)}) | |
| output$pr.num.11b <- renderText({print.string(pr.restDigit(), 11)}) | |
| output$pr.num.12a <- renderText({print.string(pr.firstDigit(),12)}) | |
| output$pr.num.12b <- renderText({print.string(pr.restDigit(), 12)}) | |
| output$pr.num.13a <- renderText({print.string(pr.firstDigit(),13)}) | |
| output$pr.num.13b <- renderText({print.string(pr.restDigit(), 13)}) | |
| output$pr.num.14a <- renderText({print.string(pr.firstDigit(),14)}) | |
| output$pr.num.14b <- renderText({print.string(pr.restDigit(), 14)}) | |
| output$pr.num.15a <- renderText({print.string(pr.firstDigit(),15)}) | |
| output$pr.num.15b <- renderText({print.string(pr.restDigit(), 15)}) | |
| output$pr.num.16a <- renderText({print.string(pr.firstDigit(),16)}) | |
| output$pr.num.16b <- renderText({print.string(pr.restDigit(), 16)}) | |
| output$pr.num.17a <- renderText({print.string(pr.firstDigit(),17)}) | |
| output$pr.num.17b <- renderText({print.string(pr.restDigit(), 17)}) | |
| output$pr.num.18a <- renderText({print.string(pr.firstDigit(),18)}) | |
| output$pr.num.18b <- renderText({print.string(pr.restDigit(), 18)}) | |
| output$pr.num.19a <- renderText({print.string(pr.firstDigit(),19)}) | |
| output$pr.num.19b <- renderText({print.string(pr.restDigit(), 19)}) | |
| output$pr.num.20a <- renderText({print.string(pr.firstDigit(),20)}) | |
| output$pr.num.20b <- renderText({print.string(pr.restDigit(), 20)}) | |
| output$pr.num.21a <- renderText({print.string(pr.firstDigit(), 21)}) | |
| output$pr.num.21b <- renderText({print.string(pr.restDigit(), 21)}) | |
| output$pr.num.22a <- renderText({print.string(pr.firstDigit(), 22)}) | |
| output$pr.num.22b <- renderText({print.string(pr.restDigit(), 22)}) | |
| output$pr.num.23a <- renderText({print.string(pr.firstDigit(), 23)}) | |
| output$pr.num.23b <- renderText({print.string(pr.restDigit(), 23)}) | |
| output$pr.num.24a <- renderText({print.string(pr.firstDigit(), 24)}) | |
| output$pr.num.24b <- renderText({print.string(pr.restDigit(), 24)}) | |
| output$pr.num.25a <- renderText({print.string(pr.firstDigit(), 25)}) | |
| output$pr.num.25b <- renderText({print.string(pr.restDigit(), 25)}) | |
| output$pr.num.26a <- renderText({print.string(pr.firstDigit(), 26)}) | |
| output$pr.num.26b <- renderText({print.string(pr.restDigit(), 26)}) | |
| output$pr.num.27a <- renderText({print.string(pr.firstDigit(), 27)}) | |
| output$pr.num.27b <- renderText({print.string(pr.restDigit(), 27)}) | |
| output$pr.num.28a <- renderText({print.string(pr.firstDigit(), 28)}) | |
| output$pr.num.28b <- renderText({print.string(pr.restDigit(), 28)}) | |
| output$pr.num.29a <- renderText({print.string(pr.firstDigit(), 29)}) | |
| output$pr.num.29b <- renderText({print.string(pr.restDigit(), 29)}) | |
| output$pr.num.30a <- renderText({print.string(pr.firstDigit(),30)}) | |
| output$pr.num.30b <- renderText({print.string(pr.restDigit(), 30)}) | |
| output$pr.num.31a <- renderText({print.string(pr.firstDigit(), 31)}) | |
| output$pr.num.31b <- renderText({print.string(pr.restDigit(), 31)}) | |
| output$pr.num.32a <- renderText({print.string(pr.firstDigit(), 32)}) | |
| output$pr.num.32b <- renderText({print.string(pr.restDigit(), 32)}) | |
| output$pr.num.33a <- renderText({print.string(pr.firstDigit(), 33)}) | |
| output$pr.num.33b <- renderText({print.string(pr.restDigit(), 33)}) | |
| output$pr.num.34a <- renderText({print.string(pr.firstDigit(), 34)}) | |
| output$pr.num.34b <- renderText({print.string(pr.restDigit(), 34)}) | |
| output$pr.num.35a <- renderText({print.string(pr.firstDigit(), 35)}) | |
| output$pr.num.35b <- renderText({print.string(pr.restDigit(), 35)}) | |
| output$pr.num.36a <- renderText({print.string(pr.firstDigit(), 36)}) | |
| output$pr.num.36b <- renderText({print.string(pr.restDigit(), 36)}) | |
| output$pr.num.37a <- renderText({print.string(pr.firstDigit(), 37)}) | |
| output$pr.num.37b <- renderText({print.string(pr.restDigit(), 37)}) | |
| output$pr.num.38a <- renderText({print.string(pr.firstDigit(), 38)}) | |
| output$pr.num.38b <- renderText({print.string(pr.restDigit(), 38)}) | |
| output$pr.num.39a <- renderText({print.string(pr.firstDigit(), 39)}) | |
| output$pr.num.39b <- renderText({print.string(pr.restDigit(), 39)}) | |
| output$pr.num.40a <- renderText({print.string(pr.firstDigit(),40)}) | |
| output$pr.num.40b <- renderText({print.string(pr.restDigit(), 40)}) | |
| output$pr.num.41a <- renderText({print.string(pr.firstDigit(), 41)}) | |
| output$pr.num.41b <- renderText({print.string(pr.restDigit(), 41)}) | |
| output$pr.num.42a <- renderText({print.string(pr.firstDigit(), 42)}) | |
| output$pr.num.42b <- renderText({print.string(pr.restDigit(), 42)}) | |
| output$pr.num.43a <- renderText({print.string(pr.firstDigit(), 43)}) | |
| output$pr.num.43b <- renderText({print.string(pr.restDigit(), 43)}) | |
| output$pr.num.44a <- renderText({print.string(pr.firstDigit(), 44)}) | |
| output$pr.num.44b <- renderText({print.string(pr.restDigit(), 44)}) | |
| output$pr.num.45a <- renderText({print.string(pr.firstDigit(), 45)}) | |
| output$pr.num.45b <- renderText({print.string(pr.restDigit(), 45)}) | |
| output$pr.num.46a <- renderText({print.string(pr.firstDigit(), 46)}) | |
| output$pr.num.46b <- renderText({print.string(pr.restDigit(), 46)}) | |
| output$pr.num.47a <- renderText({print.string(pr.firstDigit(), 47)}) | |
| output$pr.num.47b <- renderText({print.string(pr.restDigit(), 47)}) | |
| output$pr.num.48a <- renderText({print.string(pr.firstDigit(), 48)}) | |
| output$pr.num.48b <- renderText({print.string(pr.restDigit(), 48)}) | |
| output$pr.num.49a <- renderText({print.string(pr.firstDigit(), 49)}) | |
| output$pr.num.49b <- renderText({print.string(pr.restDigit(), 49)}) | |
| output$pr.num.50a <- renderText({print.string(pr.firstDigit(),50)}) | |
| output$pr.num.50b <- renderText({print.string(pr.restDigit(), 50)}) | |
| output$pr.num.51a <- renderText({print.string(pr.firstDigit(), 51)}) | |
| output$pr.num.51b <- renderText({print.string(pr.restDigit(), 51)}) | |
| output$pr.num.52a <- renderText({print.string(pr.firstDigit(), 52)}) | |
| output$pr.num.52b <- renderText({print.string(pr.restDigit(), 52)}) | |
| output$pr.num.53a <- renderText({print.string(pr.firstDigit(), 53)}) | |
| output$pr.num.53b <- renderText({print.string(pr.restDigit(), 53)}) | |
| output$pr.num.54a <- renderText({print.string(pr.firstDigit(), 54)}) | |
| output$pr.num.54b <- renderText({print.string(pr.restDigit(), 54)}) | |
| output$pr.num.55a <- renderText({print.string(pr.firstDigit(), 55)}) | |
| output$pr.num.55b <- renderText({print.string(pr.restDigit(), 55)}) | |
| output$pr.num.56a <- renderText({print.string(pr.firstDigit(), 56)}) | |
| output$pr.num.56b <- renderText({print.string(pr.restDigit(), 56)}) | |
| output$pr.num.57a <- renderText({print.string(pr.firstDigit(), 57)}) | |
| output$pr.num.57b <- renderText({print.string(pr.restDigit(), 57)}) | |
| output$pr.num.58a <- renderText({print.string(pr.firstDigit(), 58)}) | |
| output$pr.num.58b <- renderText({print.string(pr.restDigit(), 58)}) | |
| output$pr.num.59a <- renderText({print.string(pr.firstDigit(), 59)}) | |
| output$pr.num.59b <- renderText({print.string(pr.restDigit(), 59)}) | |
| output$pr.num.60a <- renderText({print.string(pr.firstDigit(),60)}) | |
| output$pr.num.60b <- renderText({print.string(pr.restDigit(), 60)}) | |
| output$pr.num.61a <- renderText({print.string(pr.firstDigit(), 61)}) | |
| output$pr.num.61b <- renderText({print.string(pr.restDigit(), 61)}) | |
| output$pr.num.62a <- renderText({print.string(pr.firstDigit(), 62)}) | |
| output$pr.num.62b <- renderText({print.string(pr.restDigit(), 62)}) | |
| output$pr.num.63a <- renderText({print.string(pr.firstDigit(), 63)}) | |
| output$pr.num.63b <- renderText({print.string(pr.restDigit(), 63)}) | |
| output$pr.num.64a <- renderText({print.string(pr.firstDigit(), 64)}) | |
| output$pr.num.64b <- renderText({print.string(pr.restDigit(), 64)}) | |
| output$pr.num.65a <- renderText({print.string(pr.firstDigit(), 65)}) | |
| output$pr.num.65b <- renderText({print.string(pr.restDigit(), 65)}) | |
| output$pr.num.66a <- renderText({print.string(pr.firstDigit(), 66)}) | |
| output$pr.num.66b <- renderText({print.string(pr.restDigit(), 66)}) | |
| output$pr.num.67a <- renderText({print.string(pr.firstDigit(), 67)}) | |
| output$pr.num.67b <- renderText({print.string(pr.restDigit(), 67)}) | |
| output$pr.num.68a <- renderText({print.string(pr.firstDigit(), 68)}) | |
| output$pr.num.68b <- renderText({print.string(pr.restDigit(), 68)}) | |
| output$pr.num.69a <- renderText({print.string(pr.firstDigit(), 69)}) | |
| output$pr.num.69b <- renderText({print.string(pr.restDigit(), 69)}) | |
| output$pr.num.70a <- renderText({print.string(pr.firstDigit(),70)}) | |
| output$pr.num.70b <- renderText({print.string(pr.restDigit(), 70)}) | |
| output$pr.num.71a <- renderText({print.string(pr.firstDigit(), 71)}) | |
| output$pr.num.71b <- renderText({print.string(pr.restDigit(), 71)}) | |
| output$pr.num.72a <- renderText({print.string(pr.firstDigit(), 72)}) | |
| output$pr.num.72b <- renderText({print.string(pr.restDigit(), 72)}) | |
| output$pr.num.73a <- renderText({print.string(pr.firstDigit(), 73)}) | |
| output$pr.num.73b <- renderText({print.string(pr.restDigit(), 73)}) | |
| output$pr.num.74a <- renderText({print.string(pr.firstDigit(), 74)}) | |
| output$pr.num.74b <- renderText({print.string(pr.restDigit(), 74)}) | |
| output$pr.num.75a <- renderText({print.string(pr.firstDigit(), 75)}) | |
| output$pr.num.75b <- renderText({print.string(pr.restDigit(), 75)}) | |
| output$pr.num.76a <- renderText({print.string(pr.firstDigit(), 76)}) | |
| output$pr.num.76b <- renderText({print.string(pr.restDigit(), 76)}) | |
| output$pr.num.77a <- renderText({print.string(pr.firstDigit(), 77)}) | |
| output$pr.num.77b <- renderText({print.string(pr.restDigit(), 77)}) | |
| output$pr.num.78a <- renderText({print.string(pr.firstDigit(), 78)}) | |
| output$pr.num.78b <- renderText({print.string(pr.restDigit(), 78)}) | |
| output$pr.num.79a <- renderText({print.string(pr.firstDigit(), 79)}) | |
| output$pr.num.79b <- renderText({print.string(pr.restDigit(), 79)}) | |
| output$pr.num.80a <- renderText({print.string(pr.firstDigit(),80)}) | |
| output$pr.num.80b <- renderText({print.string(pr.restDigit(), 80)}) | |
| output$pr.pmf <- renderPlot({ | |
| pr.big.n <-as.integer(input$my.n) | |
| pr.pmf.compare(pr.seqInput(),pr.big.n) | |
| }) | |
| })#close withProgress | |
| })#close shinyServer | |
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| # ---------------------------------------- | |
| # App Title: Benford's Law and Sequences | |
| # Author: Jimmy Doi | |
| # ---------------------------------------- | |
| library(shinyIncubator) | |
| shinyUI(navbarPage("Benford's Law: Sequences", | |
| ################################################################################################### | |
| ## tabPanel: Additive Sequence ## | |
| ################################################################################################### | |
| tabPanel("(1) Additive Sequence", | |
| fluidPage( | |
| tags$head(tags$link(rel = "icon", type = "image/x-icon", href = | |
| "https://webresource.its.calpoly.edu/cpwebtemplate/5.0.1/common/images_html/favicon.ico")), | |
| progressInit(), | |
| # Give the page a title | |
| h3("Benford's Law: Additive Sequence"), | |
| div("Note: Please adjust width of browser if only one column is visible.",br(), | |
| HTML("<a href='http://shiny.stat.calpoly.edu/BenfordData' style='color: #DC143C' | |
| target='_blank'>[Click here for another Shiny app on Benford's Law]</a>"), | |
| style = "font-size: 9pt;color:teal"),br(), | |
| p("Consider a sequence of numbers where we fix the initial two numbers and then the | |
| value of each subsequent number is the sum of the previous two. We will call this an", | |
| tags$b("additive sequence."), | |
| "When the initial two numbers are both 1 then this yields the famous Fibonacci sequence. | |
| If you only consider the first digit of each number in an additive sequence and examine its distribution, | |
| is it the case that it closely follows ", | |
| HTML("<a href='http://mathworld.wolfram.com/BenfordsLaw.html', target='_blank'>Benford's Law</a>?"), | |
| "This app generates an additive sequence, for a given length and initial sequence numbers, | |
| and applies a goodness of fit test of the observed frequencies of first digits to Benford's Law", | |
| style="font-size:11pt"), | |
| HTML("<hr style='height: 2px; color: #BDBDBD; background-color: #D9D9D9; border: none;'>"), | |
| # Generate a row with a sidebar | |
| fluidRow( | |
| column(4,wellPanel( | |
| sliderInput("seq1", | |
| label = h5("First Sequence Number"), | |
| min = 1, max = 9, value = 1, step=1),br(), | |
| sliderInput("seq2", | |
| label = h5("Second Sequence Number"), | |
| min = 1, max = 9, value = 1, step=1),br(), | |
| sliderInput("length", | |
| label = h5(HTML("Length of sequence (<i>n</i>)")), | |
| min = 150, max = 1000, value = 150, step=50),br(), | |
| br(), br(), br(), br(), | |
| div("Shiny app by", | |
| a(href="http://statweb.calpoly.edu/jdoi/",target="_blank", | |
| "Jimmy Doi"),align="right", style = "font-size: 8pt"), | |
| div("Base R code by", | |
| a(href="http://statweb.calpoly.edu/jdoi/",target="_blank", | |
| "Jimmy Doi"),align="right", style = "font-size: 8pt"), | |
| div("Shiny source files:", | |
| a(href="https://gist.github.com/calpolystat/f4475cbfe4cc77cef168", | |
| target="_blank","GitHub Gist"),align="right", style = "font-size: 8pt"), | |
| div(a(href="http://www.statistics.calpoly.edu/shiny",target="_blank", | |
| "Cal Poly Statistics Dept Shiny Series"),align="right", style = "font-size: 8pt") | |
| )), | |
| column(8, | |
| div(span(tags$b("First 50 numbers in the sequence (first digit in"),style="font-size:9pt"), | |
| span( | |
| span("red",style="font-size:9pt; color:red; font-weight:bold"),tags$b("):", | |
| conditionalPanel("input.seq1==1 & input.seq2==1", | |
| span(HTML(" "),"[Fibonacci sequence]", | |
| style="text-align: right;color:blue;font-size:9pt;display:inline-block"), | |
| style="text-align: right;font-size:0pt;display:inline-block;"), | |
| conditionalPanel("input.seq1==2 & input.seq2==1", | |
| span(HTML(" "),"[Lucas sequence]", | |
| style="text-align: right;color:blue;font-size:9pt;display:inline-block"), | |
| style="text-align: right;font-size:0pt;display:inline-block;"),style="font-size:9pt")), | |
| style="font-size:0pt"), | |
| div( | |
| div(span(textOutput("num.1a"),style="font-size: 9pt; color:red; font-weight:bold; display:inline-block"), | |
| span(textOutput("num.1b"),style="font-size: 9pt; color:black; display:inline-block"),span(HTML(" "),style="font-size:9pt"), | |
| style="display:inline-block"), | |
| div(span(textOutput("num.2a"),style="font-size: 9pt; color:red; font-weight:bold; display:inline-block"), | |
| span(textOutput("num.2b"),style="font-size: 9pt; color:black; display:inline-block"),span(HTML(" "),style="font-size:9pt"), | |
| style="display:inline-block"), | |
| div(span(textOutput("num.3a"),style="font-size: 9pt; color:red; font-weight:bold; display:inline-block"), | |
| span(textOutput("num.3b"),style="font-size: 9pt; color:black; display:inline-block"),span(HTML(" "),style="font-size:9pt"), | |
| style="display:inline-block"), | |
| div(span(textOutput("num.4a"),style="font-size: 9pt; color:red; font-weight:bold; display:inline-block"), | |
| span(textOutput("num.4b"),style="font-size: 9pt; color:black; display:inline-block"),span(HTML(" "),style="font-size:9pt"), | |
| style="display:inline-block"), | |
| div(span(textOutput("num.5a"),style="font-size: 9pt; color:red; font-weight:bold; display:inline-block"), | |
| span(textOutput("num.5b"),style="font-size: 9pt; color:black; display:inline-block"),span(HTML(" "),style="font-size:9pt"), | |
| style="display:inline-block"), | |
| div(span(textOutput("num.6a"),style="font-size: 9pt; color:red; font-weight:bold; display:inline-block"), | |
| span(textOutput("num.6b"),style="font-size: 9pt; color:black; display:inline-block"),span(HTML(" "),style="font-size:9pt"), | |
| style="display:inline-block"), | |
| div(span(textOutput("num.7a"),style="font-size: 9pt; color:red; font-weight:bold; display:inline-block"), | |
| span(textOutput("num.7b"),style="font-size: 9pt; color:black; display:inline-block"),span(HTML(" "),style="font-size:9pt"), | |
| style="display:inline-block"), | |
| div(span(textOutput("num.8a"),style="font-size: 9pt; color:red; font-weight:bold; display:inline-block"), | |
| span(textOutput("num.8b"),style="font-size: 9pt; color:black; display:inline-block"),span(HTML(" "),style="font-size:9pt"), | |
| style="display:inline-block"), | |
| div(span(textOutput("num.9a"),style="font-size: 9pt; color:red; font-weight:bold; display:inline-block"), | |
| span(textOutput("num.9b"),style="font-size: 9pt; color:black; display:inline-block"),span(HTML(" "),style="font-size:9pt"), | |
| style="display:inline-block"), | |
| div(span(textOutput("num.10a"),style="font-size: 9pt; color:red; font-weight:bold; display:inline-block"), | |
| span(textOutput("num.10b"),style="font-size: 9pt; color:black; display:inline-block"),span(HTML(" "),style="font-size:9pt"), | |
| style="display:inline-block"), | |
| div(span(textOutput("num.11a"),style="font-size: 9pt; color:red; font-weight:bold; display:inline-block"), | |
| span(textOutput("num.11b"),style="font-size: 9pt; color:black; display:inline-block"),span(HTML(" "),style="font-size:9pt"), | |
| style="display:inline-block"), | |
| div(span(textOutput("num.12a"),style="font-size: 9pt; color:red; font-weight:bold; display:inline-block"), | |
| span(textOutput("num.12b"),style="font-size: 9pt; color:black; display:inline-block"),span(HTML(" "),style="font-size:9pt"), | |
| style="display:inline-block"), | |
| div(span(textOutput("num.13a"),style="font-size: 9pt; color:red; font-weight:bold; display:inline-block"), | |
| span(textOutput("num.13b"),style="font-size: 9pt; color:black; display:inline-block"),span(HTML(" "),style="font-size:9pt"), | |
| style="display:inline-block"), | |
| div(span(textOutput("num.14a"),style="font-size: 9pt; color:red; font-weight:bold; display:inline-block"), | |
| span(textOutput("num.14b"),style="font-size: 9pt; color:black; display:inline-block"),span(HTML(" "),style="font-size:9pt"), | |
| style="display:inline-block"), | |
| div(span(textOutput("num.15a"),style="font-size: 9pt; color:red; font-weight:bold; display:inline-block"), | |
| span(textOutput("num.15b"),style="font-size: 9pt; color:black; display:inline-block"),span(HTML(" "),style="font-size:9pt"), | |
| style="display:inline-block"), | |
| div(span(textOutput("num.16a"),style="font-size: 9pt; color:red; font-weight:bold; display:inline-block"), | |
| span(textOutput("num.16b"),style="font-size: 9pt; color:black; display:inline-block"),span(HTML(" "),style="font-size:9pt"), | |
| style="display:inline-block"), | |
| div(span(textOutput("num.17a"),style="font-size: 9pt; color:red; font-weight:bold; display:inline-block"), | |
| span(textOutput("num.17b"),style="font-size: 9pt; color:black; display:inline-block"),span(HTML(" "),style="font-size:9pt"), | |
| style="display:inline-block"), | |
| div(span(textOutput("num.18a"),style="font-size: 9pt; color:red; font-weight:bold; display:inline-block"), | |
| span(textOutput("num.18b"),style="font-size: 9pt; color:black; display:inline-block"),span(HTML(" "),style="font-size:9pt"), | |
| style="display:inline-block"), | |
| div(span(textOutput("num.19a"),style="font-size: 9pt; color:red; font-weight:bold; display:inline-block"), | |
| span(textOutput("num.19b"),style="font-size: 9pt; color:black; display:inline-block"),span(HTML(" "),style="font-size:9pt"), | |
| style="display:inline-block"), | |
| div(span(textOutput("num.20a"),style="font-size: 9pt; color:red; font-weight:bold; display:inline-block"), | |
| span(textOutput("num.20b"),style="font-size: 9pt; color:black; display:inline-block"),span(HTML(" "),style="font-size:9pt"), | |
| style="display:inline-block"), | |
| div(span(textOutput("num.21a"),style="font-size: 9pt; color:red; font-weight:bold; display:inline-block"), | |
| span(textOutput("num.21b"),style="font-size: 9pt; color:black; display:inline-block"),span(HTML(" "),style="font-size:9pt"), | |
| style="display:inline-block"), | |
| div(span(textOutput("num.22a"),style="font-size: 9pt; color:red; font-weight:bold; display:inline-block"), | |
| span(textOutput("num.22b"),style="font-size: 9pt; color:black; display:inline-block"),span(HTML(" "),style="font-size:9pt"), | |
| style="display:inline-block"), | |
| div(span(textOutput("num.23a"),style="font-size: 9pt; color:red; font-weight:bold; display:inline-block"), | |
| span(textOutput("num.23b"),style="font-size: 9pt; color:black; display:inline-block"),span(HTML(" "),style="font-size:9pt"), | |
| style="display:inline-block"), | |
| div(span(textOutput("num.24a"),style="font-size: 9pt; color:red; font-weight:bold; display:inline-block"), | |
| span(textOutput("num.24b"),style="font-size: 9pt; color:black; display:inline-block"),span(HTML(" "),style="font-size:9pt"), | |
| style="display:inline-block"), | |
| div(span(textOutput("num.25a"),style="font-size: 9pt; color:red; font-weight:bold; display:inline-block"), | |
| span(textOutput("num.25b"),style="font-size: 9pt; color:black; display:inline-block"),span(HTML(" "),style="font-size:9pt"), | |
| style="display:inline-block"), | |
| div(span(textOutput("num.26a"),style="font-size: 9pt; color:red; font-weight:bold; display:inline-block"), | |
| span(textOutput("num.26b"),style="font-size: 9pt; color:black; display:inline-block"),span(HTML(" "),style="font-size:9pt"), | |
| style="display:inline-block"), | |
| div(span(textOutput("num.27a"),style="font-size: 9pt; color:red; font-weight:bold; display:inline-block"), | |
| span(textOutput("num.27b"),style="font-size: 9pt; color:black; display:inline-block"),span(HTML(" "),style="font-size:9pt"), | |
| style="display:inline-block"), | |
| div(span(textOutput("num.28a"),style="font-size: 9pt; color:red; font-weight:bold; display:inline-block"), | |
| span(textOutput("num.28b"),style="font-size: 9pt; color:black; display:inline-block"),span(HTML(" "),style="font-size:9pt"), | |
| style="display:inline-block"), | |
| div(span(textOutput("num.29a"),style="font-size: 9pt; color:red; font-weight:bold; display:inline-block"), | |
| span(textOutput("num.29b"),style="font-size: 9pt; color:black; display:inline-block"),span(HTML(" "),style="font-size:9pt"), | |
| style="display:inline-block"), | |
| div(span(textOutput("num.30a"),style="font-size: 9pt; color:red; font-weight:bold; display:inline-block"), | |
| span(textOutput("num.30b"),style="font-size: 9pt; color:black; display:inline-block"),span(HTML(" "),style="font-size:9pt"), | |
| style="display:inline-block"), | |
| div(span(textOutput("num.31a"),style="font-size: 9pt; color:red; font-weight:bold; display:inline-block"), | |
| span(textOutput("num.31b"),style="font-size: 9pt; color:black; display:inline-block"),span(HTML(" "),style="font-size:9pt"), | |
| style="display:inline-block"), | |
| div(span(textOutput("num.32a"),style="font-size: 9pt; color:red; font-weight:bold; display:inline-block"), | |
| span(textOutput("num.32b"),style="font-size: 9pt; color:black; display:inline-block"),span(HTML(" "),style="font-size:9pt"), | |
| style="display:inline-block"), | |
| div(span(textOutput("num.33a"),style="font-size: 9pt; color:red; font-weight:bold; display:inline-block"), | |
| span(textOutput("num.33b"),style="font-size: 9pt; color:black; display:inline-block"),span(HTML(" "),style="font-size:9pt"), | |
| style="display:inline-block"), | |
| div(span(textOutput("num.34a"),style="font-size: 9pt; color:red; font-weight:bold; display:inline-block"), | |
| span(textOutput("num.34b"),style="font-size: 9pt; color:black; display:inline-block"),span(HTML(" "),style="font-size:9pt"), | |
| style="display:inline-block"), | |
| div(span(textOutput("num.35a"),style="font-size: 9pt; color:red; font-weight:bold; display:inline-block"), | |
| span(textOutput("num.35b"),style="font-size: 9pt; color:black; display:inline-block"),span(HTML(" "),style="font-size:9pt"), | |
| style="display:inline-block"), | |
| div(span(textOutput("num.36a"),style="font-size: 9pt; color:red; font-weight:bold; display:inline-block"), | |
| span(textOutput("num.36b"),style="font-size: 9pt; color:black; display:inline-block"),span(HTML(" "),style="font-size:9pt"), | |
| style="display:inline-block"), | |
| div(span(textOutput("num.37a"),style="font-size: 9pt; color:red; font-weight:bold; display:inline-block"), | |
| span(textOutput("num.37b"),style="font-size: 9pt; color:black; display:inline-block"),span(HTML(" "),style="font-size:9pt"), | |
| style="display:inline-block"), | |
| div(span(textOutput("num.38a"),style="font-size: 9pt; color:red; font-weight:bold; display:inline-block"), | |
| span(textOutput("num.38b"),style="font-size: 9pt; color:black; display:inline-block"),span(HTML(" "),style="font-size:9pt"), | |
| style="display:inline-block"), | |
| div(span(textOutput("num.39a"),style="font-size: 9pt; color:red; font-weight:bold; display:inline-block"), | |
| span(textOutput("num.39b"),style="font-size: 9pt; color:black; display:inline-block"),span(HTML(" "),style="font-size:9pt"), | |
| style="display:inline-block"), | |
| div(span(textOutput("num.40a"),style="font-size: 9pt; color:red; font-weight:bold; display:inline-block"), | |
| span(textOutput("num.40b"),style="font-size: 9pt; color:black; display:inline-block"),span(HTML(" "),style="font-size:9pt"), | |
| style="display:inline-block"), | |
| div(span(textOutput("num.41a"),style="font-size: 9pt; color:red; font-weight:bold; display:inline-block"), | |
| span(textOutput("num.41b"),style="font-size: 9pt; color:black; display:inline-block"),span(HTML(" "),style="font-size:9pt"), | |
| style="display:inline-block"), | |
| div(span(textOutput("num.42a"),style="font-size: 9pt; color:red; font-weight:bold; display:inline-block"), | |
| span(textOutput("num.42b"),style="font-size: 9pt; color:black; display:inline-block"),span(HTML(" "),style="font-size:9pt"), | |
| style="display:inline-block"), | |
| div(span(textOutput("num.43a"),style="font-size: 9pt; color:red; font-weight:bold; display:inline-block"), | |
| span(textOutput("num.43b"),style="font-size: 9pt; color:black; display:inline-block"),span(HTML(" "),style="font-size:9pt"), | |
| style="display:inline-block"), | |
| div(span(textOutput("num.44a"),style="font-size: 9pt; color:red; font-weight:bold; display:inline-block"), | |
| span(textOutput("num.44b"),style="font-size: 9pt; color:black; display:inline-block"),span(HTML(" "),style="font-size:9pt"), | |
| style="display:inline-block"), | |
| div(span(textOutput("num.45a"),style="font-size: 9pt; color:red; font-weight:bold; display:inline-block"), | |
| span(textOutput("num.45b"),style="font-size: 9pt; color:black; display:inline-block"),span(HTML(" "),style="font-size:9pt"), | |
| style="display:inline-block"), | |
| div(span(textOutput("num.46a"),style="font-size: 9pt; color:red; font-weight:bold; display:inline-block"), | |
| span(textOutput("num.46b"),style="font-size: 9pt; color:black; display:inline-block"),span(HTML(" "),style="font-size:9pt"), | |
| style="display:inline-block"), | |
| div(span(textOutput("num.47a"),style="font-size: 9pt; color:red; font-weight:bold; display:inline-block"), | |
| span(textOutput("num.47b"),style="font-size: 9pt; color:black; display:inline-block"),span(HTML(" "),style="font-size:9pt"), | |
| style="display:inline-block"), | |
| div(span(textOutput("num.48a"),style="font-size: 9pt; color:red; font-weight:bold; display:inline-block"), | |
| span(textOutput("num.48b"),style="font-size: 9pt; color:black; display:inline-block"),span(HTML(" "),style="font-size:9pt"), | |
| style="display:inline-block"), | |
| div(span(textOutput("num.49a"),style="font-size: 9pt; color:red; font-weight:bold; display:inline-block"), | |
| span(textOutput("num.49b"),style="font-size: 9pt; color:black; display:inline-block"),span(HTML(" "),style="font-size:9pt"), | |
| style="display:inline-block"), | |
| div(span(textOutput("num.50a"),style="font-size: 9pt; color:red; font-weight:bold; display:inline-block"), | |
| span(textOutput("num.50b"),style="font-size: 9pt; color:black; display:inline-block"),span(HTML(" "),style="font-size:9pt"), | |
| span("",style="font-size: 9pt"),style="display:inline-block"), | |
| style="font-size:0;"), | |
| div(span("[Sequence has ",style="text-align: right;font-size:9pt;display:inline-block"), | |
| span(HTML(" "),style="text-align: right;font-size:9pt"), | |
| span(textOutput("textlength"),style="text-align: right;font-size:9pt;display:inline-block;color:teal"), | |
| span(HTML(" "),style="text-align: right;font-size:9pt"), | |
| span("numbers total]",style="text-align: right;font-size:9pt;display:inline-block"), | |
| style="text-align: right;font-size:0pt;display:inline-block;"), | |
| HTML("<hr style='height: 2px; color: #de7008; background-color: #df7109; border: none;'>"), | |
| fluidRow( | |
| column(4, | |
| p(tags$b("Goodness of Fit Test")), | |
| verbatimTextOutput("goodness")), | |
| column(8, | |
| plotOutput("pmf") | |
| )#closes column-8 | |
| ),#closes fluidRow | |
| HTML("<hr style='height: 2px; color: #de7008; background-color: #df7109; border: none;'>") | |
| ) # closes column-8 | |
| ) #closes fluidRow | |
| ) #closes fluidPage | |
| ), #close tabPanel#1 | |
| ################################################################################################### | |
| ## tabPanel: Power Sequence ## | |
| ################################################################################################### | |
| tabPanel("(2) Power Sequence", | |
| fluidPage( | |
| # Give the page a title | |
| h3("Benford's Law: Power Sequence"), | |
| div("Note: Please adjust width of browser if only one column is visible.",br(), | |
| HTML("<a href='https://calpolystat.shinyapps.io/BenfordData', | |
| target='_blank'>[Click here for another Shiny app on Benford's Law]</a>"), | |
| style = "font-size: 9pt;color:teal"),br(), | |
| p("Consider a sequence of the form", | |
| HTML("<i>b<sup>1</sup></i>, <i>b<sup>2</sup></i>, …, <i>b<sup> n</sup></i>, "), | |
| "where ", tags$em("b"), "is called the base. | |
| We will call this a ", HTML("<b>power sequence</b>."), " | |
| If you only consider the first digit of each number in a power sequence and examine its distribution, | |
| is it the case that it closely follows ", | |
| HTML("<a href='http://mathworld.wolfram.com/BenfordsLaw.html', target='_blank'>Benford's Law</a>?"), | |
| "This app generates the power sequence, for a given", HTML("<i>b</i> and <i>n</i>,"), | |
| "and applies a goodness of fit test of the observed frequencies of first digits to Benford's Law.", | |
| style="font-size:11pt"), | |
| HTML("<hr style='height: 2px; color: #BDBDBD; background-color: #D9D9D9; border: none;'>"), | |
| fluidRow( | |
| column(4,wellPanel( | |
| sliderInput("pow.base", | |
| label = h5(HTML("Base value (<i>b</i>)")), | |
| min = 2, max = 9, value = 2, step=1),br(), | |
| sliderInput("pow.length", | |
| label = h5(HTML("Length of sequence (<i>n</i>)")), | |
| min = 150, max = 300, value = 150, step=10),br(), | |
| br(), br(), br(), br(), | |
| div("Shiny app by", | |
| a(href="http://statweb.calpoly.edu/jdoi/",target="_blank", | |
| "Jimmy Doi"),align="right", style = "font-size: 8pt"), | |
| div("Base R code by", | |
| a(href="http://statweb.calpoly.edu/jdoi/",target="_blank", | |
| "Jimmy Doi"),align="right", style = "font-size: 8pt"), | |
| div("Shiny source files:", | |
| a(href="https://gist.github.com/calpolystat/f4475cbfe4cc77cef168", | |
| target="_blank","GitHub Gist"),align="right", style = "font-size: 8pt"), | |
| div(a(href="http://www.statistics.calpoly.edu/shiny",target="_blank", | |
| "Cal Poly Statistics Dept Shiny Series"),align="right", style = "font-size: 8pt") | |
| )), | |
| column(8, | |
| div(span(tags$b("First 20 numbers in the sequence (first digit in"),style="font-size:9pt"), | |
| span( | |
| span("red",style="font-size:9pt; color:red; font-weight:bold"),tags$b("):",style="font-size:9pt")), | |
| style="font-size:0pt"), | |
| div( | |
| div(span(textOutput("e.num.1a"),style="font-size: 9pt; color:red; font-weight:bold; display:inline-block"), | |
| span(textOutput("e.num.1b"),style="font-size: 9pt; color:black; display:inline-block"),span(HTML(" "),style="font-size:9pt"), | |
| style="display:inline-block"), | |
| div(span(textOutput("e.num.2a"),style="font-size: 9pt; color:red; font-weight:bold; display:inline-block"), | |
| span(textOutput("e.num.2b"),style="font-size: 9pt; color:black; display:inline-block"),span(HTML(" "),style="font-size:9pt"), | |
| style="display:inline-block"), | |
| div(span(textOutput("e.num.3a"),style="font-size: 9pt; color:red; font-weight:bold; display:inline-block"), | |
| span(textOutput("e.num.3b"),style="font-size: 9pt; color:black; display:inline-block"),span(HTML(" "),style="font-size:9pt"), | |
| style="display:inline-block"), | |
| div(span(textOutput("e.num.4a"),style="font-size: 9pt; color:red; font-weight:bold; display:inline-block"), | |
| span(textOutput("e.num.4b"),style="font-size: 9pt; color:black; display:inline-block"),span(HTML(" "),style="font-size:9pt"), | |
| style="display:inline-block"), | |
| div(span(textOutput("e.num.5a"),style="font-size: 9pt; color:red; font-weight:bold; display:inline-block"), | |
| span(textOutput("e.num.5b"),style="font-size: 9pt; color:black; display:inline-block"),span(HTML(" "),style="font-size:9pt"), | |
| style="display:inline-block"), | |
| div(span(textOutput("e.num.6a"),style="font-size: 9pt; color:red; font-weight:bold; display:inline-block"), | |
| span(textOutput("e.num.6b"),style="font-size: 9pt; color:black; display:inline-block"),span(HTML(" "),style="font-size:9pt"), | |
| style="display:inline-block"), | |
| div(span(textOutput("e.num.7a"),style="font-size: 9pt; color:red; font-weight:bold; display:inline-block"), | |
| span(textOutput("e.num.7b"),style="font-size: 9pt; color:black; display:inline-block"),span(HTML(" "),style="font-size:9pt"), | |
| style="display:inline-block"), | |
| div(span(textOutput("e.num.8a"),style="font-size: 9pt; color:red; font-weight:bold; display:inline-block"), | |
| span(textOutput("e.num.8b"),style="font-size: 9pt; color:black; display:inline-block"),span(HTML(" "),style="font-size:9pt"), | |
| style="display:inline-block"), | |
| div(span(textOutput("e.num.9a"),style="font-size: 9pt; color:red; font-weight:bold; display:inline-block"), | |
| span(textOutput("e.num.9b"),style="font-size: 9pt; color:black; display:inline-block"),span(HTML(" "),style="font-size:9pt"), | |
| style="display:inline-block"), | |
| div(span(textOutput("e.num.10a"),style="font-size: 9pt; color:red; font-weight:bold; display:inline-block"), | |
| span(textOutput("e.num.10b"),style="font-size: 9pt; color:black; display:inline-block"),span(HTML(" "),style="font-size:9pt"), | |
| style="display:inline-block"), | |
| div(span(textOutput("e.num.11a"),style="font-size: 9pt; color:red; font-weight:bold; display:inline-block"), | |
| span(textOutput("e.num.11b"),style="font-size: 9pt; color:black; display:inline-block"),span(HTML(" "),style="font-size:9pt"), | |
| style="display:inline-block"), | |
| div(span(textOutput("e.num.12a"),style="font-size: 9pt; color:red; font-weight:bold; display:inline-block"), | |
| span(textOutput("e.num.12b"),style="font-size: 9pt; color:black; display:inline-block"),span(HTML(" "),style="font-size:9pt"), | |
| style="display:inline-block"), | |
| div(span(textOutput("e.num.13a"),style="font-size: 9pt; color:red; font-weight:bold; display:inline-block"), | |
| span(textOutput("e.num.13b"),style="font-size: 9pt; color:black; display:inline-block"),span(HTML(" "),style="font-size:9pt"), | |
| style="display:inline-block"), | |
| div(span(textOutput("e.num.14a"),style="font-size: 9pt; color:red; font-weight:bold; display:inline-block"), | |
| span(textOutput("e.num.14b"),style="font-size: 9pt; color:black; display:inline-block"),span(HTML(" "),style="font-size:9pt"), | |
| style="display:inline-block"), | |
| div(span(textOutput("e.num.15a"),style="font-size: 9pt; color:red; font-weight:bold; display:inline-block"), | |
| span(textOutput("e.num.15b"),style="font-size: 9pt; color:black; display:inline-block"),span(HTML(" "),style="font-size:9pt"), | |
| style="display:inline-block"), | |
| div(span(textOutput("e.num.16a"),style="font-size: 9pt; color:red; font-weight:bold; display:inline-block"), | |
| span(textOutput("e.num.16b"),style="font-size: 9pt; color:black; display:inline-block"),span(HTML(" "),style="font-size:9pt"), | |
| style="display:inline-block"), | |
| div(span(textOutput("e.num.17a"),style="font-size: 9pt; color:red; font-weight:bold; display:inline-block"), | |
| span(textOutput("e.num.17b"),style="font-size: 9pt; color:black; display:inline-block"),span(HTML(" "),style="font-size:9pt"), | |
| style="display:inline-block"), | |
| div(span(textOutput("e.num.18a"),style="font-size: 9pt; color:red; font-weight:bold; display:inline-block"), | |
| span(textOutput("e.num.18b"),style="font-size: 9pt; color:black; display:inline-block"),span(HTML(" "),style="font-size:9pt"), | |
| style="display:inline-block"), | |
| div(span(textOutput("e.num.19a"),style="font-size: 9pt; color:red; font-weight:bold; display:inline-block"), | |
| span(textOutput("e.num.19b"),style="font-size: 9pt; color:black; display:inline-block"),span(HTML(" "),style="font-size:9pt"), | |
| style="display:inline-block"), | |
| div(span(textOutput("e.num.20a"),style="font-size: 9pt; color:red; font-weight:bold; display:inline-block"), | |
| span(textOutput("e.num.20b"),style="font-size: 9pt; color:black; display:inline-block"),span(HTML(" "),style="font-size:9pt"), | |
| span("",style="font-size: 9pt"),style="display:inline-block"), | |
| style="font-size:0;"), | |
| div(span("[Sequence has ",style="font-size:9pt;display:inline-block"), | |
| span(HTML(" "),style="font-size:9pt"), | |
| span(textOutput("powlength"),style="font-size:9pt;display:inline-block;color:teal"), | |
| span(HTML(" "),style="font-size:9pt"), | |
| span("numbers total]",style="font-size:9pt;display:inline-block"),style="font-size:0pt;display:inline-block;",align="right"), | |
| HTML("<hr style='height: 2px; color: #de7008; background-color: #df7109; border: none;'>"), | |
| fluidRow( | |
| column(4, | |
| p(tags$b("Goodness of Fit Test")), | |
| verbatimTextOutput("e.goodness")), | |
| column(8, | |
| plotOutput("e.pmf") | |
| ) #closes column-8 | |
| ), #closes fluidRow | |
| HTML("<hr style='height: 2px; color: #de7008; background-color: #df7109; border: none;'>") | |
| ) #closes column-8 | |
| ) #closes fluidRow | |
| ) #closes fluidPage | |
| ), #close tabPanel#2 | |
| ################################################################################################### | |
| ## tabPanel: Prime Numbers Sequence ## | |
| ################################################################################################### | |
| tabPanel("(3) Prime Numbers Sequence", | |
| fluidPage( | |
| # Give the page a title | |
| h3("Generalized Benford's Law: Prime Numbers Sequence"), | |
| div("Note: Please adjust width of browser if only one column is visible.",br(), | |
| HTML("<a href='https://calpolystat.shinyapps.io/BenfordData', | |
| target='_blank'>[Click here for another Shiny app on Benford's Law]</a>"), | |
| style = "font-size: 9pt;color:teal"),br(), | |
| p("Consider the sequence of prime numbers less than or equal to some power of 10. An article from 2009 | |
| shows that the distribution of the first digit of these prime numbers | |
| is well described by what's known as", HTML("<b>Generalized Benford's Law (GBL)</b>"),". | |
| This app generates the prime numbers less than or equal to", HTML("10<sup>3</sup>, 10<sup>4</sup>, | |
| 10<sup>5</sup>, or 10<sup>6</sup>"), "and applies a goodness of fit test of the observed frequencies of first digits to GBL." | |
| ), | |
| p("More information on the Generalized Benford's Law can be found in the following journal article:"), | |
| div("Luque, B. and Lacasa, L.(2009)", | |
| HTML("'<a href='http://rspa.royalsocietypublishing.org/content/465/2107/2197.abstract?sid=25124ad9-160f-432e-afe9-17b04ae725d1', | |
| target='_blank'>The first-digit frequencies of prime numbers and Riemann zeta zeros</a>'"), | |
| em("Proc. R. Soc. A"),", 465, 2197-2216", style="padding-left: 20px; display:block; border-left: 5px solid #faebbc;margin-left:0px"), | |
| HTML("<hr style='height: 2px; color: #BDBDBD; background-color: #D9D9D9; border: none;'>"), | |
| # Generate a row with a sidebar | |
| fluidRow( | |
| column(4,wellPanel( | |
| selectInput("my.n", label = h5("Generate sequence of prime numbers less than or equal to"), | |
| choices = list("1,000" = 1000, "10,000" = 10000, "100,000" = 100000, "1,000,000" = 1000000), | |
| selected = 1000), | |
| br(), br(), br(), br(), | |
| div("Shiny app by", | |
| a(href="http://statweb.calpoly.edu/jdoi/",target="_blank", | |
| "Jimmy Doi"),align="right", style = "font-size: 8pt"), | |
| div("Base R code by", | |
| a(href="http://statweb.calpoly.edu/jdoi/",target="_blank", | |
| "Jimmy Doi"),align="right", style = "font-size: 8pt"), | |
| div("Shiny source files:", | |
| a(href="https://gist.github.com/calpolystat/f4475cbfe4cc77cef168", | |
| target="_blank","GitHub Gist"),align="right", style = "font-size: 8pt"), | |
| div(a(href="http://www.statistics.calpoly.edu/shiny",target="_blank", | |
| "Cal Poly Statistics Dept Shiny Series"),align="right", style = "font-size: 8pt") | |
| )), | |
| column(8, | |
| div(span(tags$b("First 80 numbers in the sequence (first digit in"),style="font-size:9pt"), | |
| span( | |
| span("red",style="font-size:9pt; color:red; font-weight:bold"),tags$b("):",style="font-size:9pt")), | |
| style="font-size:0pt"), | |
| div( | |
| div(span(textOutput("pr.num.1a"),style="font-size: 9pt; color:red; font-weight:bold; display:inline-block"), | |
| span(textOutput("pr.num.1b"),style="font-size: 9pt; color:black; display:inline-block"),span(HTML(" "),style="font-size:9pt"), | |
| style="display:inline-block"), | |
| div(span(textOutput("pr.num.2a"),style="font-size: 9pt; color:red; font-weight:bold; display:inline-block"), | |
| span(textOutput("pr.num.2b"),style="font-size: 9pt; color:black; display:inline-block"),span(HTML(" "),style="font-size:9pt"), | |
| style="display:inline-block"), | |
| div(span(textOutput("pr.num.3a"),style="font-size: 9pt; color:red; font-weight:bold; display:inline-block"), | |
| span(textOutput("pr.num.3b"),style="font-size: 9pt; color:black; display:inline-block"),span(HTML(" "),style="font-size:9pt"), | |
| style="display:inline-block"), | |
| div(span(textOutput("pr.num.4a"),style="font-size: 9pt; color:red; font-weight:bold; display:inline-block"), | |
| span(textOutput("pr.num.4b"),style="font-size: 9pt; color:black; display:inline-block"),span(HTML(" "),style="font-size:9pt"), | |
| style="display:inline-block"), | |
| div(span(textOutput("pr.num.5a"),style="font-size: 9pt; color:red; font-weight:bold; display:inline-block"), | |
| span(textOutput("pr.num.5b"),style="font-size: 9pt; color:black; display:inline-block"),span(HTML(" "),style="font-size:9pt"), | |
| style="display:inline-block"), | |
| div(span(textOutput("pr.num.6a"),style="font-size: 9pt; color:red; font-weight:bold; display:inline-block"), | |
| span(textOutput("pr.num.6b"),style="font-size: 9pt; color:black; display:inline-block"),span(HTML(" "),style="font-size:9pt"), | |
| style="display:inline-block"), | |
| div(span(textOutput("pr.num.7a"),style="font-size: 9pt; color:red; font-weight:bold; display:inline-block"), | |
| span(textOutput("pr.num.7b"),style="font-size: 9pt; color:black; display:inline-block"),span(HTML(" "),style="font-size:9pt"), | |
| style="display:inline-block"), | |
| div(span(textOutput("pr.num.8a"),style="font-size: 9pt; color:red; font-weight:bold; display:inline-block"), | |
| span(textOutput("pr.num.8b"),style="font-size: 9pt; color:black; display:inline-block"),span(HTML(" "),style="font-size:9pt"), | |
| style="display:inline-block"), | |
| div(span(textOutput("pr.num.9a"),style="font-size: 9pt; color:red; font-weight:bold; display:inline-block"), | |
| span(textOutput("pr.num.9b"),style="font-size: 9pt; color:black; display:inline-block"),span(HTML(" "),style="font-size:9pt"), | |
| style="display:inline-block"), | |
| div(span(textOutput("pr.num.10a"),style="font-size: 9pt; color:red; font-weight:bold; display:inline-block"), | |
| span(textOutput("pr.num.10b"),style="font-size: 9pt; color:black; display:inline-block"),span(HTML(" "),style="font-size:9pt"), | |
| style="display:inline-block"), | |
| div(span(textOutput("pr.num.11a"),style="font-size: 9pt; color:red; font-weight:bold; display:inline-block"), | |
| span(textOutput("pr.num.11b"),style="font-size: 9pt; color:black; display:inline-block"),span(HTML(" "),style="font-size:9pt"), | |
| style="display:inline-block"), | |
| div(span(textOutput("pr.num.12a"),style="font-size: 9pt; color:red; font-weight:bold; display:inline-block"), | |
| span(textOutput("pr.num.12b"),style="font-size: 9pt; color:black; display:inline-block"),span(HTML(" "),style="font-size:9pt"), | |
| style="display:inline-block"), | |
| div(span(textOutput("pr.num.13a"),style="font-size: 9pt; color:red; font-weight:bold; display:inline-block"), | |
| span(textOutput("pr.num.13b"),style="font-size: 9pt; color:black; display:inline-block"),span(HTML(" "),style="font-size:9pt"), | |
| style="display:inline-block"), | |
| div(span(textOutput("pr.num.14a"),style="font-size: 9pt; color:red; font-weight:bold; display:inline-block"), | |
| span(textOutput("pr.num.14b"),style="font-size: 9pt; color:black; display:inline-block"),span(HTML(" "),style="font-size:9pt"), | |
| style="display:inline-block"), | |
| div(span(textOutput("pr.num.15a"),style="font-size: 9pt; color:red; font-weight:bold; display:inline-block"), | |
| span(textOutput("pr.num.15b"),style="font-size: 9pt; color:black; display:inline-block"),span(HTML(" "),style="font-size:9pt"), | |
| style="display:inline-block"), | |
| div(span(textOutput("pr.num.16a"),style="font-size: 9pt; color:red; font-weight:bold; display:inline-block"), | |
| span(textOutput("pr.num.16b"),style="font-size: 9pt; color:black; display:inline-block"),span(HTML(" "),style="font-size:9pt"), | |
| style="display:inline-block"), | |
| div(span(textOutput("pr.num.17a"),style="font-size: 9pt; color:red; font-weight:bold; display:inline-block"), | |
| span(textOutput("pr.num.17b"),style="font-size: 9pt; color:black; display:inline-block"),span(HTML(" "),style="font-size:9pt"), | |
| style="display:inline-block"), | |
| div(span(textOutput("pr.num.18a"),style="font-size: 9pt; color:red; font-weight:bold; display:inline-block"), | |
| span(textOutput("pr.num.18b"),style="font-size: 9pt; color:black; display:inline-block"),span(HTML(" "),style="font-size:9pt"), | |
| style="display:inline-block"), | |
| div(span(textOutput("pr.num.19a"),style="font-size: 9pt; color:red; font-weight:bold; display:inline-block"), | |
| span(textOutput("pr.num.19b"),style="font-size: 9pt; color:black; display:inline-block"),span(HTML(" "),style="font-size:9pt"), | |
| style="display:inline-block"), | |
| div(span(textOutput("pr.num.20a"),style="font-size: 9pt; color:red; font-weight:bold; display:inline-block"), | |
| span(textOutput("pr.num.20b"),style="font-size: 9pt; color:black; display:inline-block"),span(HTML(" "),style="font-size:9pt"), | |
| style="display:inline-block"), | |
| div(span(textOutput("pr.num.21a"),style="font-size: 9pt; color:red; font-weight:bold; display:inline-block"), | |
| span(textOutput("pr.num.21b"),style="font-size: 9pt; color:black; display:inline-block"),span(HTML(" "),style="font-size:9pt"), | |
| style="display:inline-block"), | |
| div(span(textOutput("pr.num.22a"),style="font-size: 9pt; color:red; font-weight:bold; display:inline-block"), | |
| span(textOutput("pr.num.22b"),style="font-size: 9pt; color:black; display:inline-block"),span(HTML(" "),style="font-size:9pt"), | |
| style="display:inline-block"), | |
| div(span(textOutput("pr.num.23a"),style="font-size: 9pt; color:red; font-weight:bold; display:inline-block"), | |
| span(textOutput("pr.num.23b"),style="font-size: 9pt; color:black; display:inline-block"),span(HTML(" "),style="font-size:9pt"), | |
| style="display:inline-block"), | |
| div(span(textOutput("pr.num.24a"),style="font-size: 9pt; color:red; font-weight:bold; display:inline-block"), | |
| span(textOutput("pr.num.24b"),style="font-size: 9pt; color:black; display:inline-block"),span(HTML(" "),style="font-size:9pt"), | |
| style="display:inline-block"), | |
| div(span(textOutput("pr.num.25a"),style="font-size: 9pt; color:red; font-weight:bold; display:inline-block"), | |
| span(textOutput("pr.num.25b"),style="font-size: 9pt; color:black; display:inline-block"),span(HTML(" "),style="font-size:9pt"), | |
| style="display:inline-block"), | |
| div(span(textOutput("pr.num.26a"),style="font-size: 9pt; color:red; font-weight:bold; display:inline-block"), | |
| span(textOutput("pr.num.26b"),style="font-size: 9pt; color:black; display:inline-block"),span(HTML(" "),style="font-size:9pt"), | |
| style="display:inline-block"), | |
| div(span(textOutput("pr.num.27a"),style="font-size: 9pt; color:red; font-weight:bold; display:inline-block"), | |
| span(textOutput("pr.num.27b"),style="font-size: 9pt; color:black; display:inline-block"),span(HTML(" "),style="font-size:9pt"), | |
| style="display:inline-block"), | |
| div(span(textOutput("pr.num.28a"),style="font-size: 9pt; color:red; font-weight:bold; display:inline-block"), | |
| span(textOutput("pr.num.28b"),style="font-size: 9pt; color:black; display:inline-block"),span(HTML(" "),style="font-size:9pt"), | |
| style="display:inline-block"), | |
| div(span(textOutput("pr.num.29a"),style="font-size: 9pt; color:red; font-weight:bold; display:inline-block"), | |
| span(textOutput("pr.num.29b"),style="font-size: 9pt; color:black; display:inline-block"),span(HTML(" "),style="font-size:9pt"), | |
| style="display:inline-block"), | |
| div(span(textOutput("pr.num.30a"),style="font-size: 9pt; color:red; font-weight:bold; display:inline-block"), | |
| span(textOutput("pr.num.30b"),style="font-size: 9pt; color:black; display:inline-block"),span(HTML(" "),style="font-size:9pt"), | |
| style="display:inline-block"), | |
| div(span(textOutput("pr.num.31a"),style="font-size: 9pt; color:red; font-weight:bold; display:inline-block"), | |
| span(textOutput("pr.num.31b"),style="font-size: 9pt; color:black; display:inline-block"),span(HTML(" "),style="font-size:9pt"), | |
| style="display:inline-block"), | |
| div(span(textOutput("pr.num.32a"),style="font-size: 9pt; color:red; font-weight:bold; display:inline-block"), | |
| span(textOutput("pr.num.32b"),style="font-size: 9pt; color:black; display:inline-block"),span(HTML(" "),style="font-size:9pt"), | |
| style="display:inline-block"), | |
| div(span(textOutput("pr.num.33a"),style="font-size: 9pt; color:red; font-weight:bold; display:inline-block"), | |
| span(textOutput("pr.num.33b"),style="font-size: 9pt; color:black; display:inline-block"),span(HTML(" "),style="font-size:9pt"), | |
| style="display:inline-block"), | |
| div(span(textOutput("pr.num.34a"),style="font-size: 9pt; color:red; font-weight:bold; display:inline-block"), | |
| span(textOutput("pr.num.34b"),style="font-size: 9pt; color:black; display:inline-block"),span(HTML(" "),style="font-size:9pt"), | |
| style="display:inline-block"), | |
| div(span(textOutput("pr.num.35a"),style="font-size: 9pt; color:red; font-weight:bold; display:inline-block"), | |
| span(textOutput("pr.num.35b"),style="font-size: 9pt; color:black; display:inline-block"),span(HTML(" "),style="font-size:9pt"), | |
| style="display:inline-block"), | |
| div(span(textOutput("pr.num.36a"),style="font-size: 9pt; color:red; font-weight:bold; display:inline-block"), | |
| span(textOutput("pr.num.36b"),style="font-size: 9pt; color:black; display:inline-block"),span(HTML(" "),style="font-size:9pt"), | |
| style="display:inline-block"), | |
| div(span(textOutput("pr.num.37a"),style="font-size: 9pt; color:red; font-weight:bold; display:inline-block"), | |
| span(textOutput("pr.num.37b"),style="font-size: 9pt; color:black; display:inline-block"),span(HTML(" "),style="font-size:9pt"), | |
| style="display:inline-block"), | |
| div(span(textOutput("pr.num.38a"),style="font-size: 9pt; color:red; font-weight:bold; display:inline-block"), | |
| span(textOutput("pr.num.38b"),style="font-size: 9pt; color:black; display:inline-block"),span(HTML(" "),style="font-size:9pt"), | |
| style="display:inline-block"), | |
| div(span(textOutput("pr.num.39a"),style="font-size: 9pt; color:red; font-weight:bold; display:inline-block"), | |
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| style="display:inline-block"), | |
| div(span(textOutput("pr.num.40a"),style="font-size: 9pt; color:red; font-weight:bold; display:inline-block"), | |
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| style="display:inline-block"), | |
| div(span(textOutput("pr.num.41a"),style="font-size: 9pt; color:red; font-weight:bold; display:inline-block"), | |
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| style="display:inline-block"), | |
| div(span(textOutput("pr.num.42a"),style="font-size: 9pt; color:red; font-weight:bold; display:inline-block"), | |
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| style="display:inline-block"), | |
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| style="display:inline-block"), | |
| div(span(textOutput("pr.num.44a"),style="font-size: 9pt; color:red; font-weight:bold; display:inline-block"), | |
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| style="display:inline-block"), | |
| div(span(textOutput("pr.num.45a"),style="font-size: 9pt; color:red; font-weight:bold; display:inline-block"), | |
| span(textOutput("pr.num.45b"),style="font-size: 9pt; color:black; display:inline-block"),span(HTML(" "),style="font-size:9pt"), | |
| style="display:inline-block"), | |
| div(span(textOutput("pr.num.46a"),style="font-size: 9pt; color:red; font-weight:bold; display:inline-block"), | |
| span(textOutput("pr.num.46b"),style="font-size: 9pt; color:black; display:inline-block"),span(HTML(" "),style="font-size:9pt"), | |
| style="display:inline-block"), | |
| div(span(textOutput("pr.num.47a"),style="font-size: 9pt; color:red; font-weight:bold; display:inline-block"), | |
| span(textOutput("pr.num.47b"),style="font-size: 9pt; color:black; display:inline-block"),span(HTML(" "),style="font-size:9pt"), | |
| style="display:inline-block"), | |
| div(span(textOutput("pr.num.48a"),style="font-size: 9pt; color:red; font-weight:bold; display:inline-block"), | |
| span(textOutput("pr.num.48b"),style="font-size: 9pt; color:black; display:inline-block"),span(HTML(" "),style="font-size:9pt"), | |
| style="display:inline-block"), | |
| div(span(textOutput("pr.num.49a"),style="font-size: 9pt; color:red; font-weight:bold; display:inline-block"), | |
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| style="display:inline-block"), | |
| div(span(textOutput("pr.num.50a"),style="font-size: 9pt; color:red; font-weight:bold; display:inline-block"), | |
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| style="display:inline-block"), | |
| div(span(textOutput("pr.num.51a"),style="font-size: 9pt; color:red; font-weight:bold; display:inline-block"), | |
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| style="display:inline-block"), | |
| div(span(textOutput("pr.num.52a"),style="font-size: 9pt; color:red; font-weight:bold; display:inline-block"), | |
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| style="display:inline-block"), | |
| div(span(textOutput("pr.num.53a"),style="font-size: 9pt; color:red; font-weight:bold; display:inline-block"), | |
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| style="display:inline-block"), | |
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| style="display:inline-block"), | |
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| style="display:inline-block"), | |
| div(span(textOutput("pr.num.59a"),style="font-size: 9pt; color:red; font-weight:bold; display:inline-block"), | |
| span(textOutput("pr.num.59b"),style="font-size: 9pt; color:black; display:inline-block"),span(HTML(" "),style="font-size:9pt"), | |
| style="display:inline-block"), | |
| div(span(textOutput("pr.num.60a"),style="font-size: 9pt; color:red; font-weight:bold; display:inline-block"), | |
| span(textOutput("pr.num.60b"),style="font-size: 9pt; color:black; display:inline-block"),span(HTML(" "),style="font-size:9pt"), | |
| style="display:inline-block"), | |
| div(span(textOutput("pr.num.61a"),style="font-size: 9pt; color:red; font-weight:bold; display:inline-block"), | |
| span(textOutput("pr.num.61b"),style="font-size: 9pt; color:black; display:inline-block"),span(HTML(" "),style="font-size:9pt"), | |
| style="display:inline-block"), | |
| div(span(textOutput("pr.num.62a"),style="font-size: 9pt; color:red; font-weight:bold; display:inline-block"), | |
| span(textOutput("pr.num.62b"),style="font-size: 9pt; color:black; display:inline-block"),span(HTML(" "),style="font-size:9pt"), | |
| style="display:inline-block"), | |
| div(span(textOutput("pr.num.63a"),style="font-size: 9pt; color:red; font-weight:bold; display:inline-block"), | |
| span(textOutput("pr.num.63b"),style="font-size: 9pt; color:black; display:inline-block"),span(HTML(" "),style="font-size:9pt"), | |
| style="display:inline-block"), | |
| div(span(textOutput("pr.num.64a"),style="font-size: 9pt; color:red; font-weight:bold; display:inline-block"), | |
| span(textOutput("pr.num.64b"),style="font-size: 9pt; color:black; display:inline-block"),span(HTML(" "),style="font-size:9pt"), | |
| style="display:inline-block"), | |
| div(span(textOutput("pr.num.65a"),style="font-size: 9pt; color:red; font-weight:bold; display:inline-block"), | |
| span(textOutput("pr.num.65b"),style="font-size: 9pt; color:black; display:inline-block"),span(HTML(" "),style="font-size:9pt"), | |
| style="display:inline-block"), | |
| div(span(textOutput("pr.num.66a"),style="font-size: 9pt; color:red; font-weight:bold; display:inline-block"), | |
| span(textOutput("pr.num.66b"),style="font-size: 9pt; color:black; display:inline-block"),span(HTML(" "),style="font-size:9pt"), | |
| style="display:inline-block"), | |
| div(span(textOutput("pr.num.67a"),style="font-size: 9pt; color:red; font-weight:bold; display:inline-block"), | |
| span(textOutput("pr.num.67b"),style="font-size: 9pt; color:black; display:inline-block"),span(HTML(" "),style="font-size:9pt"), | |
| style="display:inline-block"), | |
| div(span(textOutput("pr.num.68a"),style="font-size: 9pt; color:red; font-weight:bold; display:inline-block"), | |
| span(textOutput("pr.num.68b"),style="font-size: 9pt; color:black; display:inline-block"),span(HTML(" "),style="font-size:9pt"), | |
| style="display:inline-block"), | |
| div(span(textOutput("pr.num.69a"),style="font-size: 9pt; color:red; font-weight:bold; display:inline-block"), | |
| span(textOutput("pr.num.69b"),style="font-size: 9pt; color:black; display:inline-block"),span(HTML(" "),style="font-size:9pt"), | |
| style="display:inline-block"), | |
| div(span(textOutput("pr.num.70a"),style="font-size: 9pt; color:red; font-weight:bold; display:inline-block"), | |
| span(textOutput("pr.num.70b"),style="font-size: 9pt; color:black; display:inline-block"),span(HTML(" "),style="font-size:9pt"), | |
| style="display:inline-block"), | |
| div(span(textOutput("pr.num.71a"),style="font-size: 9pt; color:red; font-weight:bold; display:inline-block"), | |
| span(textOutput("pr.num.71b"),style="font-size: 9pt; color:black; display:inline-block"),span(HTML(" "),style="font-size:9pt"), | |
| style="display:inline-block"), | |
| div(span(textOutput("pr.num.72a"),style="font-size: 9pt; color:red; font-weight:bold; display:inline-block"), | |
| span(textOutput("pr.num.72b"),style="font-size: 9pt; color:black; display:inline-block"),span(HTML(" "),style="font-size:9pt"), | |
| style="display:inline-block"), | |
| div(span(textOutput("pr.num.73a"),style="font-size: 9pt; color:red; font-weight:bold; display:inline-block"), | |
| span(textOutput("pr.num.73b"),style="font-size: 9pt; color:black; display:inline-block"),span(HTML(" "),style="font-size:9pt"), | |
| style="display:inline-block"), | |
| div(span(textOutput("pr.num.74a"),style="font-size: 9pt; color:red; font-weight:bold; display:inline-block"), | |
| span(textOutput("pr.num.74b"),style="font-size: 9pt; color:black; display:inline-block"),span(HTML(" "),style="font-size:9pt"), | |
| style="display:inline-block"), | |
| div(span(textOutput("pr.num.75a"),style="font-size: 9pt; color:red; font-weight:bold; display:inline-block"), | |
| span(textOutput("pr.num.75b"),style="font-size: 9pt; color:black; display:inline-block"),span(HTML(" "),style="font-size:9pt"), | |
| style="display:inline-block"), | |
| div(span(textOutput("pr.num.76a"),style="font-size: 9pt; color:red; font-weight:bold; display:inline-block"), | |
| span(textOutput("pr.num.76b"),style="font-size: 9pt; color:black; display:inline-block"),span(HTML(" "),style="font-size:9pt"), | |
| style="display:inline-block"), | |
| div(span(textOutput("pr.num.77a"),style="font-size: 9pt; color:red; font-weight:bold; display:inline-block"), | |
| span(textOutput("pr.num.77b"),style="font-size: 9pt; color:black; display:inline-block"),span(HTML(" "),style="font-size:9pt"), | |
| style="display:inline-block"), | |
| div(span(textOutput("pr.num.78a"),style="font-size: 9pt; color:red; font-weight:bold; display:inline-block"), | |
| span(textOutput("pr.num.78b"),style="font-size: 9pt; color:black; display:inline-block"),span(HTML(" "),style="font-size:9pt"), | |
| style="display:inline-block"), | |
| div(span(textOutput("pr.num.79a"),style="font-size: 9pt; color:red; font-weight:bold; display:inline-block"), | |
| span(textOutput("pr.num.79b"),style="font-size: 9pt; color:black; display:inline-block"),span(HTML(" "),style="font-size:9pt"), | |
| style="display:inline-block"), | |
| div(span(textOutput("pr.num.80a"),style="font-size: 9pt; color:red; font-weight:bold; display:inline-block"), | |
| span(textOutput("pr.num.80b"),style="font-size: 9pt; color:black; display:inline-block"),span(HTML(" "),style="font-size:9pt"), | |
| style="display:inline-block"), | |
| style="font-size:0;"), | |
| div(span("[Sequence has ",style="font-size:9pt;display:inline-block"), | |
| span(HTML(" "),style="font-size:9pt"), | |
| span(textOutput("num.primes"),style="font-size:9pt;display:inline-block;color:teal"), | |
| span(HTML(" "),style="font-size:9pt"), | |
| span("prime numbers total]",style="font-size:9pt;display:inline-block"),style="font-size:0pt;display:inline-block;",align="right"), | |
| HTML("<hr style='height: 2px; color: #de7008; background-color: #df7109; border: none;'>"), | |
| fluidRow( | |
| column(4, | |
| p(tags$b("Goodness of Fit Test")), | |
| verbatimTextOutput("pr.goodness")), | |
| column(8, | |
| plotOutput("pr.pmf") | |
| ) # closes column-8 | |
| ), #closes fluidRow | |
| HTML("<hr style='height: 2px; color: #de7008; background-color: #df7109; border: none;'>") | |
| ) #closes column-8 | |
| ) #closes fluidRow | |
| ) #closes fluidPage | |
| ) #closes tabPanel#3 | |
| ) #closes navbarPage | |
| ) #closes shinyUI |
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