kprime.RdThe 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) .
pkprime(x, nu1, nu2, ncp)
dkprime(x, nu1, nu2, ncp)
qkprime(p, nu1, nu2, ncp)the value from which a probability is sought;
the first degree of freedom;
the second degree of freedom;
the noncentrality parameter;
the probability from which a quantile is requested;
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.
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.
dkprime(11.1, 9, 8, 10.0) # 0.09410193
#> [1] 0.09410193
pkprime(11.1, 9, 8, 10.0) # 0.606652
#> [1] 0.6066524
qkprime(0.01, 9, 8, 10.0) # 3.875234
#> [1] 3.875234