simulateSampDist: Simulated sampling distribution of mean or other statistic
In jhmaindonald/DAAG: Data Analysis and Graphics Data and Functions

Description Usage Arguments Value Author(s) References See Also Examples

Simulates the sample distribution of the specified statistic, for samples of the size(s) specified in numINsamp. Additionally a with replacement) sample is drawn from the specified population.

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simulateSampDist(rpop = rnorm, numsamp = 100, numINsamp = c(4, 16),
                 FUN = mean, seed=NULL
      )

`rpop`	Either a function that generates random samples from the specified distribution, or a vector of values that define the population (i.e., an empirical distribution)
`numsamp`	Number of samples that should be taken. For close approximation of the asymptotic distribution (e.g., for the mean) this number should be large
`numINsamp`	Size(s) of each of the `numsamp` sample(s)
`FUN`	Function to calculate the statistic whose sampling distribution is to be simulated
`seed`	Optional seed for random number generation

List, with elements values, numINsamp and FUN

`values`	Matrix, with dimensions `numsamp` by `numINsamp + 1`. The first column has a random with replacement sample from the population, while the remaining `length(numINsamp)` columns hold simulated values from sampling distributions with samples of the specified size(s)
`numINsamp`	Input value of `numINsamp`
`numsamp`	Input value of `numsamp`

John Maindonald

Maindonald, J.H. and Braun, W.J. (3rd edn, 2010) Data Analysis and Graphics Using R, 3rd edn, Sections 3.3 and 3.4

help(plotSampDist)

## By default, sample from normal population
simAvs <- simulateSampDist()
par(pty="s")
plotSampDist(simAvs)
## Sample from empirical distribution
simAvs <- simulateSampDist(rpop=rivers)
plotSampDist(simAvs)


## The function is currently defined as
function(rpop=rnorm, numsamp=100, numINsamp=c(4,16), FUN=mean,
seed=NULL){
    if(!is.null(seed))set.seed(seed)
    funtxt <- deparse(substitute(FUN))
    nDists <- length(numINsamp)+1
    values <- matrix(0, nrow=numsamp, ncol=nDists)
    if(!is.function(rpop)) {
      x <- rpop
      rpop <- function(n)sample(x, n, replace=TRUE)
    }
    values[,1] <- rpop(numsamp)
    for(j in 2:nDists){
      n <- numINsamp[j-1]
      for(i in 1:numsamp)values[i, j] <- FUN(rpop(n))
    }
    colnames(values) <- paste("Size", c(1, numINsamp))
    invisible(list(values=values, numINsamp=numINsamp, FUN=funtxt))
  }