Shiny application to fit a beta curve given the median and 90th percentile.

server.R

library(shiny)

shinyServer(function(input, output) {

  output$distPlot <- renderPlot({
   
    library(LearnBayes)
    quantile1 = list(p=.5, x=input$p50)
    quantile2 = list(p=.9, x=input$p90)
    ab = beta.select(quantile1, quantile2)
    curve(dbeta(x, ab[1], ab[2]), 0, 1, ylab="Density",
          main=paste("a = ",ab[1]," b = ", ab[2]))
  })

  output$summary <- renderPrint( {
    library(LearnBayes)
    quantile1 = list(p=.5, x=input$p50)
    quantile2 = list(p=.9, x=input$p90)
    ab = beta.select(quantile1, quantile2)
    q = qbeta(c(0.05, 0.25, 0.50, 0.75, 0.95), 
             ab[1], ab[2])
    names(q) = c("5th Percentile", "Lower Quartile",
             "Median", "Upper Quartile", "95th Percentile")
  q
  })


})

ui.R

library(shiny)

# Define UI for application that plots random distributions 
shinyUI(pageWithSidebar(

  # Application title
  headerPanel("Beta Curve"),

  # Sidebar with a slider input for number of observations
  sidebarPanel(
    sliderInput("p50", 
                "Median of beta curve:", 
                min = 0, 
                max = 1, 
                value = 0.5),
    sliderInput("p90", 
                "90th Percentile:", 
                min = 0, 
                max = 1, 
                value = 0.8)
  ),

  # Show a plot of the generated distribution
  mainPanel(
    plotOutput("distPlot") ,
    verbatimTextOutput("summary")
  )
))