kprime {CohensdpLibrary}

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