Scatterplots for differently shaped random distributions

norta.R

#Source: Reich Seiter, http://rpubs.com/rseiter/50148
#NORmal-To-Anything (NORTA) Algorithm Examples

#Context: http://blog.ouseful.info/2014/12/17/sketching-scatterplots-to-demonstrate-different-correlations/

# Create a multi-variate <dist> distribution with <samples> samples and correlation <r>
# Distribution names as in help("Distributions")
# The distribution names are used to form the quantile function name q<dist>
# Currently additional arguments to the quantile function are not supported
corrdata <- function(samples=200, r=0, dist="norm"){
  data = mvrnorm(n=samples, mu=c(0, 0), Sigma=matrix(c(1, r, r, 1), nrow=2), empirical=TRUE)
  distfunname <- paste0("q", dist)
  if (!exists(distfunname)) { error(paste("Function", distfunname, "does not exist")) }
  
  # Convert the multi-variate normal variables to the desired distribution using NORTA
  data <- eval(parse(text=paste0(distfunname, "(pnorm(data))")))
  
  # Check that the correlation has not changed
  writeLines(paste("Desired correlation for dist", dist, "was", r,
              "  Actual correlation was", round(cor(data)[1,2],3)))
  
  data.frame(x=data[,1], y=data[,2])
}

plotcorrdata <- function(samples=200, dist="norm") {
  df <- data.frame()
  for (i in c(1,0.8,0.5,0.2,0,-0.2,-0.5,-0.8,-1)) {
    tmp <- corrdata(samples, i, dist)
    tmp['corr'] <- i
    df <- rbind(df, tmp)
  }
  
  g <- ggplot(df, aes(x=x,y=y)) + geom_point(size=1)
  g <- g + facet_wrap(~corr) + stat_smooth(method='lm',se=FALSE,color='red')
  g <- g + coord_fixed() +  ggtitle(paste("Scatterplots for Correlated", dist, "Random Variables"))
  plot(g)
}

dists <- c("norm", "unif", "exp")

for (dist in dists) {
  plotcorrdata(samples=200, dist=dist)
}