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On the computation and inversion of the cumulative noncentral beta distribution function

Abstract: The computation and inversion of the noncentral beta distribution Bp,q(x, y) (or the noncentral F-distribution, a particular case of Bp,q(x, y)) play an important role in different applications. In this paper we study the stability of recursions satisfied by Bp,q(x, y) and its complementary function and describe asymptotic expansions useful for computing the function when the parameters are large. We also consider the inversion problem of finding x or y when a value of Bp,q(x, y) is given. We provide approximations to x and y which can be used as starting values of methods for solving nonlinear equations (such as Newton) if higher accuracy is needed.

 Fuente: Applied Mathematics and Computation Volume 361, 15 November 2019, Pages 74-86

Editorial: Elsevier Inc.

 Fecha de publicación: 29/05/2019

Nº de páginas: 25

Tipo de publicación: Artículo de Revista

 DOI: 10.1016/j.amc.2019.05.014

ISSN: 0096-3003,1873-5649

Proyecto español: MTM2015-67142-P (MINECO/FEDER, UE) ; PGC2018-098279-B-I00 (MCIU/AEI/FEDER, UE).

Url de la publicación: https://doi.org/10.1016/j.amc.2019.05.014