server.R

# server.R

library("shiny")
library("ggplot2")    # Grammar of Graphics for plots
library("VGAM")       # Vector Generalized Linear and Additive Models
library("eeptools")   # Convenience functions for education data

shinyServer(
  function(input,output){

    mydat <- reactive({
      mydat <- rskewnorm(  # old name rsnorm()
      input$obs
        , location = input$mean
        , scale = input$variance
        , shape = input$skew
      )
      if(input$mode==input$mean){
        return(mydat)
      } else if (input$mode!=input$mean) {
        a <- table(as.vector(round(mydat)))
        m <- names(a)[a==max(a)]
        v <- max(a)
        mydat2 <- mydat[round(mydat)!=as.numeric(m)]
        samp <- sample(mydat[round(mydat)==as.numeric(m)],v*0.8)
        mydat2 <- c(mydat2,samp)
        fill <- rep(input$mode,(v-length(samp)))
        mydat <- c(mydat2,fill)
        return(mydat)
      }
    })
  
    output$distPlot<-renderPlot({
        p <- qplot(mydat(), geom = 'blank')
        p <- p + geom_line(aes(y = ..density.., colour = 'Empirical'), stat = 'density')
        p <- p + stat_function(fun = dnorm, aes(colour = 'Normal'))
        p <- p + geom_histogram(aes(y = ..density..), alpha = 0.4, binwidth = 0.2)
        p <- p + scale_colour_manual(name = 'Density', values = c('red', 'blue'))
        p <- p + theme_dpi()
        p <- p + theme(legend.position = c(0.85, 0.85))
        p <- p + xlim(c(-10,10))
        p <- p + labs(x = "data", y = "density", title = "Distribution of Data")
        print(p)
    })
  
})

ui.R

# https://gist.github.com/dgrapov/6147592
# https://gist.github.com/jknowles/4484886

# ui.R

library("shiny")
library("ggplot2")    # Grammar of Graphics for plots
library("VGAM")       # Vector Generalized Linear and Additive Models
library("eeptools")   # Convenience functions for education data

shinyUI(
  pageWithSidebar(
    headerPanel("Exploring Properties of Distributions")
    ,
    sidebarPanel(
      sliderInput("obs"
        , "Number of tries:"
        , min = 200
        , max = 5000
        , value = 500
        , step = 250
      )
      ,
      sliderInput("mean"
        , "Mean of the Distribution"
        , min = -10
        , max = 10
        , value = 0
        , step = 1
      )
      ,
      sliderInput("mode"
        , "Mode of the Distribution"
        , min = -10
        , max = 10
        , value = 0
        , step = 1
      )
      ,
      sliderInput("variance"
        , "Variance of the Distribution"
        , min = 1
        , max = 5
        , value = 1
        , step = 1
      )
      ,
      sliderInput("skew"
        , "skew of the Distribution"
        , min = -5
        , max = 5
        , value = 0
        , step = 1
      )  
    )
    ,
    mainPanel(plotOutput("distPlot"))
  )
)

played around with app by jknowles, noticed rsnorm(), from package VGAM, appears to have been renamed rskewnorm(), the above is updated to reflect that, very nice apps, thanks for sharing!