Random samples from Kolmogorov distribution

Generate random samples from Kolmogorov distribution.

psi.rks(n, df, randgen = runif, cdf = punif, ...)

Arguments

n	number of observations.
df	degrees of freedom of the Kolmogorov distribution
randgen	a function or a name of one that generates random numbers from the hypothesised distribution.
cdf	the cdf of the hypothesised distribution.
...	parameters to be passed down to randgen and cdf

Details

Instances of the \(D_{df}\) statistic are obtained by generating random samples of length df from the hypothesised distribution and computing \(D_{df}\) on them.

In the case of a simple null hypothesis from a continuous distribution the distribution of the statistic does not depend on the underlying distribution. So, only the arguments n and df are really necessary for the Kolmogorov-Smirnov test. Imaginative settings for this argument may be used to generate samples in the case of composite hypotheses.

Value

a numeric vector representing a sample from the distribution of the Kolmogorov statistic for the specified distribution.

See also

psi.pks

Examples

x1 <- psi.rks(1000,10)
hist(x1)

plot(ecdf(x1))                   # simulation estimate of the dist of D_10

f1 <- function(x) psi.pks(x,10)
curve(f1,0,1,col="blue",add=TRUE)  # overlay the exact cdf