kprime {CohensdpLibrary} | R Documentation |

## The K' or non-central K distribution.

### Description

The K' distribution was created to solve various problems in linear model statistics. pkprime returns the cumulative probability of the lambda prime distribution with parameters nu1, nu2, ncp; dkprime returns its density and qkprime, a quantile. Lecoutre (1999); Poitevineau and Lecoutre (2010).

### Usage

```
pkprime(x, nu1, nu2, ncp)
dkprime(x, nu1, nu2, ncp)
qkprime(p, nu1, nu2, ncp)
```

### Arguments

`x` |
the value from which a probability is sought; |

`nu1` |
the first degree of freedom; |

`nu2` |
the second degree of freedom; |

`ncp` |
the noncentrality parameter; |

`p` |
the probability from which a quantile is requested; |

### Details

kprime is a p,d,q set of functions that compute the K-prime distribution. This distribution has many applications,
including to obtain the sampling distribution of *r* given a population rho and the predictive distributions
of rho given a sample *r*. See Lecoutre (1999); Poitevineau and Lecoutre (2010).

These functions are herein implemented from the FORTRAN source code of Poitevineau and Lecoutre (2010).
Note that the library *sadists* also implements this distribution (Pav 2020).
However, the sadists::kprime distribution is inaccurate for small nu1 or small nu2.

### Value

The probability or quantile of a K' distribution.

### References

Lecoutre B (1999).
“Two useful distributions for Bayesian predictive procedures under normal models.”
*Journal of Statistical Planning and Inference*, **79**, 93 – 105.
doi:10.1016/S0378-3758(98)00231-6.

Pav SE (2020).
“sadists: Some Additional Distributions [R package].”
https://github.com/shabbychef/sadists.

Poitevineau J, Lecoutre B (2010).
“Implementing Bayesian predictive procedures: The K-prime and K-square distributions.”
*Computational Statistics and Data Analysis*, **54**, 724 – 731.
doi:10.1016/j.csda.2008.11.004.

Poitevineau J, Lecoutre B (2010).
“Statistical distributions for bayesian experimental data analysis fortran functions 1. continuous distributions.”
https://eris62.eu.

### Examples

```
dkprime(11.1, 9, 8, 10.0) # 0.09410193
pkprime(11.1, 9, 8, 10.0) # 0.606652
qkprime(0.01, 9, 8, 10.0) # 3.875234
```

*CohensdpLibrary*version 0.5.10 Index]