# dkay: 'dkay' The density function of the K distribution In qqtest: Self Calibrating Quantile-Quantile Plots for Visual Testing

## Description

The K density function on `df` degrees of freedom and 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` ```dkay(x, df, ncp = 0, log.p = FALSE) ```

## Arguments

 `x` A vector of values at which to calculate the density. `df` Degrees of freedom (non-negative, but can be non-integer). `ncp` Non-centrality parameter (non-negative). `log.p` logical; if `TRUE`, probabilities are given as log(p).

## Value

`dkay` gives the density evaluated at the values of `x`.

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

The length of the result is the maximum of the lengths of the numerical arguments for the other functions.

The numerical arguments are recycled to the length of the result. Only the first elements of the logical arguments are used.

## Note

All calls depend on analogous calls to chi-squared functions. See `dchisq` for details on non-centrality parameter calculations.

## Examples

 ```1 2 3 4``` ```dkay(1, 20) # # See also the vignette on the "K-distribution" # ```

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