Initial commit

README.md

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+Central Limit Theorem
+========================================================
+
+This is a simple Shiny web application using R demonstrating the Central Limit Theorem.
+

server.R

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+library(shiny)
+
+shinyServer(function(input, output) {
+
+  data <- reactive({      
+    if (input$dist=="rpois") {
+      vals <-  do.call(input$dist, list(n=input$n, lambda=1))
+    }
+    else {
+      vals <-  do.call(input$dist, list(n=input$n))
+    }
+    return (list(fun=input$dist, vals=vals))
+  })
+
+  output$plot <- renderPlot({
+    distname <- switch(input$dist,
+                       rexp = "Exponential distribution", # (n = ",
+                       rnorm = "Normal distribution", # (n = ",
+                       rlnorm = "Log-normal distribution", # (n = ",
+                       runif = "Uniform distribution", # (n = ",
+                       rpois = "Poisson distribution",
+                       rcauchy = "Cauchy distribution") # (n = ")
+
+    n <- input$n
+    k <- input$k
+    pdist <- data()$vals
+
+    if (input$dist=="rpois") {
+      x <- replicate(k, do.call(input$dist, list(n=n, lambda=1)))
+    }
+    else {
+      x <- replicate(k, do.call(input$dist, list(n=n)))
+    }
+    ndist <- rowMeans(x)
+    expect <- switch(input$dist,
+                     rexp = c(1^-1, 1^-2),
+                     rnorm = c(0, 1),
+                     rlnorm = c(exp(0+(1/2)*1^2), exp(0 + 1^2)*(exp(1^2)-1)),
+                     runif = c(0.5, (1/12)*1),
+                     rpois =c(1, 1),
+                     rcauchy = rep(NA, 2))
+    obs <- data.frame(pdist=c(mean(pdist), var(pdist)), ndist=c(mean(ndist), 
+                                                                var(ndist)))
+
+    par(mfrow=c(2,1))
+    pdens=density(pdist)
+    phist=hist(pdist, freq=FALSE, plot=FALSE)
+    hist(pdist, main=paste(n, " observations from ", distname, sep=""), 
+         xlab="Values", freq=FALSE, ylim=c(0, max(pdens$y, phist$density)))
+    lines(pdens, col="red", lwd=2)
+    abline(v=obs$pdist[1], col="blue", lwd=2, lty=2)
+    abline(v=expect[1], col="red", lwd=2, lty=2)
+    legend(x="topright", col=c("blue", "red"), lwd=2, lty=2, 
+           legend=c("Observed", "Expected"))
+    box()
+
+    ndens=density(ndist)
+    nhist=hist(ndist, freq=FALSE, plot=FALSE)
+    hist(ndist, main=paste("Distribution of mean values from ", k, 
+                           " random variables each\nconsisting of ", n, 
+                           " observations from ", distname, sep=""), 
+         xlab="Values", freq=FALSE, ylim=c(0, max(ndens$y, nhist$density)))
+    lines(ndens, col="red", lwd=2)
+    abline(v=obs$ndist[1], col="blue", lwd=2, lty=2)
+    abline(v=expect[1], col="red",  lwd=2, lty=2)
+    legend(x="topright", col=c("blue", "red"), lwd=2, lty=2, 
+           legend=c("Observed", "Expected"))
+    box()
+
+  })
+})

ui.R

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+library(shiny)
+
+shinyUI(pageWithSidebar(
+
+  headerPanel("Central Limit Theorem"),
+
+  sidebarPanel(
+    radioButtons("dist", "Parent distribution:",
+                 list("Exponential" = "rexp",
+                      "Normal" = "rnorm",
+                      "Log-normal" = "rlnorm",
+                      "Uniform" = "runif",
+                      "Poisson" = "rpois",
+                      "Cauchy (pathological: momentless)" = "rcauchy")),
+    br(),
+
+    sliderInput("n", 
+                "Number of observations from parent distribution:", 
+                value = 500,
+                min = 2, 
+                max = 1000),
+    br(),
+
+    sliderInput("k", 
+                "Number of random variables sampled from parent distribution:", 
+                value = 10,
+                min = 2, 
+                max = 400)
+  ),
+
+  mainPanel(
+    plotOutput("plot", height="900px")
+  )
+))