The Asymptotic and Numerical Inversion of the Marcum Q-Function

Gil Gómez, Amparo; Segura Sala, José Javier; Temme, Nicolaas Maria

doi:10.1111/sapm.12050

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Identificadores

URI: http://hdl.handle.net/10902/8061

DOI: 10.1111/sapm.12050

ISSN: 0022-2526

ISSN: 1467-9590

Fecha

2014

Derechos

This is the peer reviewed version of the following article:The Asymptotic and Numerical Inversion of the Marcum Q-Function. Studies in Applied Mathematics, Volume 133, Issue 2, pages 257–278, August 2014, which has been published in final form at https://doi.org/10.1111/sapm.12050. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Self-Archiving.

Publicado en

Studies in Applied Mathematics Volume 133, Issue 2, pages 257–278, August 2014

Editorial

Blackwell Publishing Ltd

Enlace a la publicación

http://dx7nk9sl6m.search.serialssolutions.com/?sid=opac&issn=0022-2526&title=1467-9590

Resumen/Abstract

The generalized Marcum functions appear in problems of technical and scientific areas such as, for example, radar detection and communications. In mathematical statistics and probability theory these functions are called the noncentral gamma or the noncentral chi-squared cumulative distribution functions. In this paper, we describe a new asymptotic method for inverting the generalized Marcum Q-function and for the complementary Marcum P-function. Also, we show how monotonicity and convexity properties of these functions can be used to find initial values for reliable Newton or secant methods to invert the function. We present details of numerical computations that show the reliability of the asymptotic approximations.