lprime {CohensdpLibrary}

Lambda prime or noncentral Lambda distribution.

Description

plprime computes the cumulative probability of the lambda-prime distribution with parameters nu, ncp. dlprime(x, nu, ncp) returns the density of the lambda prime and distribution qlprime(p, nu, ncp) its quantiles. See Lecoutre (1999).

Usage

plprime(x, nu, ncp) 
dlprime(x, nu, ncp)
qlprime(p, nu, ncp)

Arguments

x

the score for which a probability is sought;

nu

the degree of freedom of the distribution;

ncp

the non-centrality parameter of the distribution;

p

the probability from which a quantile is requested;

Details

lprime are functions that compute the Lambda-prime distribution. It was shown to be the predictive distribution of a population standardized mean or standardized mean difference in between-group design given an observed Cohen's dp (Lecoutre 2007).

These functions are implemented from the FORTRAN source of Poitevineau and Lecoutre (2010). Note that the library sadists also implements this distribution sadists::lprime (Pav 2020).

Value

     The probability or quantile of a Lambda' 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.

Lecoutre B (2007). “Another look at confidence intervals from the noncentral T distribution.” Journal of Modern Applied Statistical Methods, 6, 107 – 116. doi:10.22237/jmasm/1177992600.

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

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

Examples

dlprime(11.1, 9, 10.0) # 0.129447
plprime(11.1, 9, 10.0) # 0.7134134
qlprime(0.01, 9, 10.0) # 4.2453