Means of distributions (Standard normal vs standard Cauchy)

Define functions

## Define a function to plot for Cauchy distribution
PlotCauchy <- function(n = 100, ...) {

    ## Create n random variables from Cauchy distribution
    vecRCauchy <- rcauchy(n = n)

    ## Cumulative sum
    vecRCauchyCumSum <- cumsum(vecRCauchy)

    ## Cumulative mean
    vecRCauchyCumMean <- vecRCauchyCumSum/seq_along(vecRCauchyCumSum)

    ## Plot
    plot(vecRCauchyCumMean, ylab = "", ...)
}

## Define a function to plot for Cauchy distribution
PlotNormal <- function(n = 100, ...) {

    ## Create n random variables from Normal distribution
    vecRNormal <- rnorm(n = n)

    ## Cumulative sum
    vecRNormalCumSum <- cumsum(vecRNormal)

    ## Cumulative mean
    vecRNormalCumMean <- vecRNormalCumSum/seq_along(vecRNormalCumSum)

    ## Plot
    plot(vecRNormalCumMean, ylab = "", ...)
}

Plot cumulative means

## Layout of plots
layout(matrix(1:2, ncol = 2))

## Number of random variables
n <- 10^6

## Plot for normal distribution (mean = 0)
PlotNormal(n = n, ylim = c(-20,20))

## Plot for Cauchy distribution (mean undefined)
PlotCauchy(n = n, ylim = c(-20,20))

plot of chunk unnamed-chunk-3