In dswalter/stats250: An Interactive Environment for Learning Statistics

The Uniform distribution is a probability distribution where, unlike the Normal or Binomial, the probability is equal across the entire range.

As the range increases, the probability of landing in any one area decreases, because the probability of all regions needs to sum up to 1 (this is true of all probability distributions) and that probability of 1 now needs to be stretched across a wider area.

Density

Change the values for maximum and minimum of the uniform random variable, and you can see how it changes.

library(ggplot2)


sliderInput("range","Range of the uniform density",min=-2,max=7,value=c(0,1),step=1)

renderText({paste("What we have is now a Uniform random variable with a minimum of ", input$range[1], " and a maximum of ", input$range[2],", which we abbreviate as U(",input$range[1],",",input$range[2],"). ",sep="")})


renderText({paste("The height of the density is 1/(the width of the interval), or in this case, 1/(",input$range[2],"-",input$range[1],")=1/",input$range[2]-input$range[1],sep="")})

rng<-seq(-2.5,7.5,0.1)
rngdf<-data.frame(rng)
unifplot<-ggplot(data=rngdf,aes(x=rng))+
   ylab("Density")+xlab("Range of values")+ggtitle("Uniform Density")+coord_cartesian(xlim=c(-2,7),ylim=c(-0.0005,1.5))

renderPlot({

    #make a normal distribution based on inputs.
    rmax<-input$range[2]
    rmin<-input$range[1]
    rlength<-rmax-rmin
    rheight<-(1/rlength)

    yvals<-dunif(x=rng,min=input$range[1],max=input$range[2])
    ydf<-data.frame(rng,yvals)
    print(unifplot+
     # geom_ribbon(data=ydf,aes(ymin=0,ymax=yvals))
    #+stat_function(fun=dchisq,args=list(df=input$df),color="black")
    geom_rect(aes_string(xmax=input$range[2],xmin=input$range[1],ymin=0,ymax=rheight))
    )
    })