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Benford's Law and Sequences: Shiny app at http://www.statistics.calpoly.edu/shiny
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
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
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.
# ----------------------------------------
# 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$my.n)
pr.pmf.compare(pr.seqInput(),pr.big.n)
})
})#close withProgress
})#close shinyServer
# ----------------------------------------
# App Title: Benford's Law and Sequences
# Author: Jimmy Doi
# ----------------------------------------
library(shinyIncubator)
shinyUI(navbarPage("Benford's Law: Sequences",
###################################################################################################
## tabPanel: Additive Sequence ##
###################################################################################################
tabPanel("(1) Additive Sequence",
fluidPage(
tags$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("&nbsp;&nbsp;&nbsp;"),"[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("&nbsp;&nbsp;&nbsp;"),"[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("&nbsp;"),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("&nbsp;"),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("&nbsp;"),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("&nbsp;"),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("&nbsp;"),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("&nbsp;"),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("&nbsp;"),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("&nbsp;"),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("&nbsp;"),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("&nbsp;"),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("&nbsp;"),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("&nbsp;"),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("&nbsp;"),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("&nbsp;"),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("&nbsp;"),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("&nbsp;"),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("&nbsp;"),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("&nbsp;"),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("&nbsp;"),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("&nbsp;"),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("&nbsp;"),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("&nbsp;"),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("&nbsp;"),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("&nbsp;"),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("&nbsp;"),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("&nbsp;"),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("&nbsp;"),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("&nbsp;"),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("&nbsp;"),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("&nbsp;"),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("&nbsp;"),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("&nbsp;"),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("&nbsp;"),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("&nbsp;"),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("&nbsp;"),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("&nbsp;"),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("&nbsp;"),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("&nbsp;"),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("&nbsp;"),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("&nbsp;"),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("&nbsp;"),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("&nbsp;"),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("&nbsp;"),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("&nbsp;"),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("&nbsp;"),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("&nbsp;"),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("&nbsp;"),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("&nbsp;"),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("&nbsp;"),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("&nbsp;"),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("&nbsp;"),style="text-align: right;font-size:9pt"),
span(textOutput("textlength"),style="text-align: right;font-size:9pt;display:inline-block;color:teal"),
span(HTML("&nbsp;"),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$b("Goodness of Fit Test")),
verbatimTextOutput("goodness")),
column(8,
plotOutput("pmf")
)#closes column-8
),#closes fluidRow
HTML("<hr style='height: 2px; color: #de7008; background-color: #df7109; border: none;'>")
) # closes column-8
) #closes fluidRow
) #closes fluidPage
), #close tabPanel#1
###################################################################################################
## tabPanel: Power Sequence ##
###################################################################################################
tabPanel("(2) Power Sequence",
fluidPage(
# Give the page a title
h3("Benford's Law: Power Sequence"),
div("Note: Please adjust width of browser if only one column is visible.",br(),
HTML("<a href='https://calpolystat.shinyapps.io/BenfordData',
target='_blank'>[Click here for another Shiny app on Benford's Law]</a>"),
style = "font-size: 9pt;color:teal"),br(),
p("Consider a sequence of the form",
HTML("<i>b<sup>1</sup></i>, <i>b<sup>2</sup></i>, &hellip;, <i>b<sup>&nbsp;n</sup></i>, "),
"where ", tags$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("&nbsp;"),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("&nbsp;"),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("&nbsp;"),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("&nbsp;"),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("&nbsp;"),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("&nbsp;"),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("&nbsp;"),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("&nbsp;"),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("&nbsp;"),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("&nbsp;"),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("&nbsp;"),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("&nbsp;"),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("&nbsp;"),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("&nbsp;"),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("&nbsp;"),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("&nbsp;"),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("&nbsp;"),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("&nbsp;"),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("&nbsp;"),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("&nbsp;"),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("&nbsp;"),style="font-size:9pt"),
span(textOutput("powlength"),style="font-size:9pt;display:inline-block;color:teal"),
span(HTML("&nbsp;"),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("&nbsp;"),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("&nbsp;"),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("&nbsp;"),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("&nbsp;"),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("&nbsp;"),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("&nbsp;"),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("&nbsp;"),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("&nbsp;"),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("&nbsp;"),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("&nbsp;"),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("&nbsp;"),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("&nbsp;"),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("&nbsp;"),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("&nbsp;"),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("&nbsp;"),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("&nbsp;"),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("&nbsp;"),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("&nbsp;"),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("&nbsp;"),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("&nbsp;"),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("&nbsp;"),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("&nbsp;"),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("&nbsp;"),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("&nbsp;"),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("&nbsp;"),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("&nbsp;"),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("&nbsp;"),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("&nbsp;"),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("&nbsp;"),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("&nbsp;"),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("&nbsp;"),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("&nbsp;"),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("&nbsp;"),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("&nbsp;"),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("&nbsp;"),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("&nbsp;"),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("&nbsp;"),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("&nbsp;"),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"),
span(textOutput("pr.num.39b"),style="font-size: 9pt; color:black; display:inline-block"),span(HTML("&nbsp;"),style="font-size:9pt"),
style="display:inline-block"),
div(span(textOutput("pr.num.40a"),style="font-size: 9pt; color:red; font-weight:bold; display:inline-block"),
span(textOutput("pr.num.40b"),style="font-size: 9pt; color:black; display:inline-block"),span(HTML("&nbsp;"),style="font-size:9pt"),
style="display:inline-block"),
div(span(textOutput("pr.num.41a"),style="font-size: 9pt; color:red; font-weight:bold; display:inline-block"),
span(textOutput("pr.num.41b"),style="font-size: 9pt; color:black; display:inline-block"),span(HTML("&nbsp;"),style="font-size:9pt"),
style="display:inline-block"),
div(span(textOutput("pr.num.42a"),style="font-size: 9pt; color:red; font-weight:bold; display:inline-block"),
span(textOutput("pr.num.42b"),style="font-size: 9pt; color:black; display:inline-block"),span(HTML("&nbsp;"),style="font-size:9pt"),
style="display:inline-block"),
div(span(textOutput("pr.num.43a"),style="font-size: 9pt; color:red; font-weight:bold; display:inline-block"),
span(textOutput("pr.num.43b"),style="font-size: 9pt; color:black; display:inline-block"),span(HTML("&nbsp;"),style="font-size:9pt"),
style="display:inline-block"),
div(span(textOutput("pr.num.44a"),style="font-size: 9pt; color:red; font-weight:bold; display:inline-block"),
span(textOutput("pr.num.44b"),style="font-size: 9pt; color:black; display:inline-block"),span(HTML("&nbsp;"),style="font-size:9pt"),
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("&nbsp;"),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("&nbsp;"),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("&nbsp;"),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("&nbsp;"),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"),
span(textOutput("pr.num.49b"),style="font-size: 9pt; color:black; display:inline-block"),span(HTML("&nbsp;"),style="font-size:9pt"),
style="display:inline-block"),
div(span(textOutput("pr.num.50a"),style="font-size: 9pt; color:red; font-weight:bold; display:inline-block"),
span(textOutput("pr.num.50b"),style="font-size: 9pt; color:black; display:inline-block"),span(HTML("&nbsp;"),style="font-size:9pt"),
style="display:inline-block"),
div(span(textOutput("pr.num.51a"),style="font-size: 9pt; color:red; font-weight:bold; display:inline-block"),
span(textOutput("pr.num.51b"),style="font-size: 9pt; color:black; display:inline-block"),span(HTML("&nbsp;"),style="font-size:9pt"),
style="display:inline-block"),
div(span(textOutput("pr.num.52a"),style="font-size: 9pt; color:red; font-weight:bold; display:inline-block"),
span(textOutput("pr.num.52b"),style="font-size: 9pt; color:black; display:inline-block"),span(HTML("&nbsp;"),style="font-size:9pt"),
style="display:inline-block"),
div(span(textOutput("pr.num.53a"),style="font-size: 9pt; color:red; font-weight:bold; display:inline-block"),
span(textOutput("pr.num.53b"),style="font-size: 9pt; color:black; display:inline-block"),span(HTML("&nbsp;"),style="font-size:9pt"),
style="display:inline-block"),
div(span(textOutput("pr.num.54a"),style="font-size: 9pt; color:red; font-weight:bold; display:inline-block"),
span(textOutput("pr.num.54b"),style="font-size: 9pt; color:black; display:inline-block"),span(HTML("&nbsp;"),style="font-size:9pt"),
style="display:inline-block"),
div(span(textOutput("pr.num.55a"),style="font-size: 9pt; color:red; font-weight:bold; display:inline-block"),
span(textOutput("pr.num.55b"),style="font-size: 9pt; color:black; display:inline-block"),span(HTML("&nbsp;"),style="font-size:9pt"),
style="display:inline-block"),
div(span(textOutput("pr.num.56a"),style="font-size: 9pt; color:red; font-weight:bold; display:inline-block"),
span(textOutput("pr.num.56b"),style="font-size: 9pt; color:black; display:inline-block"),span(HTML("&nbsp;"),style="font-size:9pt"),
style="display:inline-block"),
div(span(textOutput("pr.num.57a"),style="font-size: 9pt; color:red; font-weight:bold; display:inline-block"),
span(textOutput("pr.num.57b"),style="font-size: 9pt; color:black; display:inline-block"),span(HTML("&nbsp;"),style="font-size:9pt"),
style="display:inline-block"),
div(span(textOutput("pr.num.58a"),style="font-size: 9pt; color:red; font-weight:bold; display:inline-block"),
span(textOutput("pr.num.58b"),style="font-size: 9pt; color:black; display:inline-block"),span(HTML("&nbsp;"),style="font-size:9pt"),
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("&nbsp;"),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("&nbsp;"),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("&nbsp;"),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("&nbsp;"),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("&nbsp;"),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("&nbsp;"),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("&nbsp;"),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("&nbsp;"),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("&nbsp;"),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("&nbsp;"),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("&nbsp;"),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("&nbsp;"),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("&nbsp;"),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("&nbsp;"),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("&nbsp;"),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("&nbsp;"),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("&nbsp;"),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("&nbsp;"),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("&nbsp;"),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("&nbsp;"),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("&nbsp;"),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("&nbsp;"),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("&nbsp;"),style="font-size:9pt"),
span(textOutput("num.primes"),style="font-size:9pt;display:inline-block;color:teal"),
span(HTML("&nbsp;"),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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