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Evaluation of the Noncentral t Distribution with S‐Systems
Author(s) -
Voit E. O.,
Rust P. F.
Publication year - 1990
Publication title -
biometrical journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.108
H-Index - 63
eISSN - 1521-4036
pISSN - 0323-3847
DOI - 10.1002/bimj.4710320603
Subject(s) - mathematics , noncentral chi squared distribution , quantile , distribution (mathematics) , mathematical analysis , nonlinear system , statistics , physics , ratio distribution , asymptotic distribution , quantum mechanics , estimator
Densities, cumulatives, and quantiles of the noncentral distributions are notoriously difficult to calculate. It is shown how the noncentral t distribution is represented in the canonical S‐system form, i.e., as a set of first‐order nonlinear differential equations in which the derivative of each variable equals a difference of two products of power‐law functions. By solving the S‐system numerically one rapidly obtains densities, cumulatives, quantiles, and moments of the central and noncentral t distributions, as well as power functions for the t‐test.