kprime: The K' or non-central K distribution.

In CohensdpLibrary: Cohen's D_p Computation with Confidence Intervals

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. \insertCitel99,pl10;textualCohensdpLibrary.

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 \insertCitel99,pl10;textualCohensdpLibrary.

These functions are herein implemented from the FORTRAN source code of \insertCitepl10b;textualCohensdpLibrary. Note that the library sadists also implements this distribution \insertCitep20CohensdpLibrary. However, the sadists::kprime distribution is inaccurate for small nu1 or small nu2.

Value

     The probability or quantile of a K' distribution.

References

\insertAllCited

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 documentation built on Sept. 11, 2024, 7:55 p.m.