正規分布シミュレータのロジック部分

server.R

#
# This is the server logic of a Shiny web application. You can run the 
# application by clicking 'Run App' above.
#
# Find out more about building applications with Shiny here:
# 
#    http://shiny.rstudio.com/
#

library(shiny)
library(ggplot2)

# Define server logic required to draw a histogram
shinyServer(function(input, output) {
  # Plot histgram of random numbers follow normal distribution generated by box-muller method
  output$distPlot <- renderPlot({
    sample <- input$normalsamplenum
    Z <- sqrt(input$dispersion)*sqrt(-2*log(runif(sample)))*cos(2*pi*runif(sample))+input$mean
    hist(Z, breaks=25, col = "orange", border="white",
         xlim = c(-100,100), ylim = c(0.0, 0.03), freq = FALSE, xlab = "sample value", ylab = "density", main = "Histgram of random number generated by box-muller method")
    par(new=T)
    plot(density(Z), xlim = c(-100,100), ylim = c(0.0, 0.03), 
          main="" , col="red", xlab = "sample value", ylab = "density")
    par(new=T)
    plot(-100:100, dnorm(-100:100, mean = input$mean, sd = sqrt(input$dispersion)),
         xlim = c(-100,100), xlab = "sample value", ylab = "density", ylim = c(0.0, 0.03), type="l", col="green")
  })
  
  output$timePlot <- renderPlot({
    sample <- input$normalsamplenum
    Z <- sqrt(input$dispersion)*sqrt(-2*log(runif(sample)))*cos(2*pi*runif(sample))+input$mean
    cdf <- ecdf(Z)
    plot(cdf, xlim=c(-100, 100), ylim=c(0,1), col="blue", xlab="index", ylab="sum of density")
    par(new=T)
    plot(-100:100, pnorm(-100:100, mean = input$mean, sd=sqrt(input$dispersion))
        ,xlim=c(-100, 100), ylim=c(0,1),col="red", type = "l", xlab="index", ylab="sum of density")
  })
  
  # Plot histgram of random numbers follow exponential distribution generated by inverse function method
  output$expdistPlot <- renderPlot({
    z <- runif(input$expsamplenum)
    result <- -log(1-z)/input$rate
    hist(result, breaks=100, col="blue", border = "white",
         xlim = c(0, 3), ylim = c(0, 2000),
         main="Histgram of random number generated by exponential distribution")
  })
  
  # plot histgram of random numbers follow poisson distribution, using exponential distribution
  # poisson distribution is discrete distribution. so we can't use inverse function method.
  output$poissondistPlot <- renderPlot({
    result <- rep(0, times=input$poissonsamplenum)
    for(i in 1:input$poissonsamplenum){
      z <- rexp(100, rate = 2.5)
      s <- 0
      count <- 1
      while(s < 1){
        s <- s + z[count]
        count <- count + 1
      }
      result[i] <- count - 1
    }
    hist(result, col="green", border = "white", xlim = c(0, 15),
         main="Histgram of random number generated by poisson distribution")
  })
  
  # plot histgram of random numbers follow pareto distribution generated by inverse function method
  output$paretodistPlot <- renderPlot({
    z <- runif(input$paretosamplenum)
    x <- input$x_0
    a <- input$a
    result <- x/(1-z)^(1/a)
    hist(result[result < 10], breaks=seq(1, 10, 0.1), col="red", border = "white", ylim = c(0, 10000), 
         main="Histgram of random number generated by pareto distribution")
  })
  
  # check law of large numbers
  output$largePlot <- renderPlot({
    n <- 1:input$largeSampleNumbers
    count <- 1
    exp.value <- rep(0, times=length(n))
    for(i in n){
      z <- runif(i)
      exp.value[count] <- mean(result <- 1/(1-z)^(1/2))
      count <- count + 1
    }
    plot(exp.value, type = "l", ylim = c(0, 4), 
         col="orange", xlab = "sample number", ylab = "expected value")
  })
})