# rkay: 'rkay' The K distribution - generating pseudo-random values In qqtest: Self Calibrating Quantile-Quantile Plots for Visual Testing

## Description

Random generation for the K distribution on `df` degrees of freedom having non-centrality parameter `ncp`.

A K distribution is the square root of a chi-square divided by its degrees of freedom. That is, if x is chi-squared on m degrees of freedom, then y = sqrt(x/m) is K on m degrees of freedom. Under standard normal theory, K is the distribution of the pivotal quantity s/sigma where s is the sample standard deviation and sigma is the standard deviation parameter of the normal density. K is the natural distribution for tests and confidence intervals about sigma. K densities are more nearly symmetric than are chi-squared and concentrate near 1. As the degrees of freedom increase, they become more symmetric, more concentrated, and more nearly normally distributed.

## Usage

 `1` ```rkay(n, df, ncp = 0) ```

## Arguments

 `n` Number of observations. If `length(n) > 1`, the length is taken to be the number required. `df` Degrees of freedom (non-negative, but can be non-integer). `ncp` Non-centrality parameter (non-negative).

## Value

`rkay` returns pseudo-randomly generated values.

Invalid arguments will result in return value NaN, with a warning.

## Note

Depends on call to analogous chi-squared functions. See `rchisq` for details on non-centrality parameter calculations.

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12``` ```x <- rkay(100, 20) hist(x, main="100 observations from a K(20)") # Certainly looks like it comes from a K on 20 qqtest(x, dist="kay",df=20) # for this many degrees of freedom it looks # a lot like a gaussian (normal) distribution qqtest(x, dist="gau",df=1) # But not like it came from a K on 1 degree of freedom qqtest(x, dist="kay",df=1) # # See the vignette for more on the "K-distribution" # ```

qqtest documentation built on March 26, 2020, 7:57 p.m.