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Algorithm 939: Computation of the Marcum Q-function

Abstract: Methods and an algorithm for computing the generalized Marcum Q.function (QƒÊ(x, y)) and the complementary function (PƒÊ(x, y)) are described. These functions appear in problems of different technical and scientific areas such as, for example, radar detection and communications, statistics and probability theory, where they are called the non-central chi-square or the non central gamma cumulative distribution functions. The algorithm for computing the Marcum functions combines different methods of evaluation in different regions: series expansions, integral representations, asymptotic expansions, and use of three-term homogeneous recurrence relations. A relative accuracy close to 10.12 can be obtained in the parameter region (x, y, ƒÊ) ¸ [0, A] ~ [0, A] ~ [1, A], A = 200, while for larger parameters the accuracy decreases (close to 10.11 for A = 1000 and close to 5 ~ 10.11 for A = 10000).

Otras publicaciones de la misma revista o congreso con autores/as de la Universidad de Cantabria

 Autoría: Gil A., Segura J., Temme N.M.,

 Fuente: ACM Transactions on Mathematical Software, Vol. 40, No. 3, Article 20, Publication date: April 2014.

Editorial: Association for Computing Machinery (ACM)

 Año de publicación: 2014

Nº de páginas: 21

Tipo de publicación: Artículo de Revista

 DOI: 10.1145/2591004

ISSN: 0098-3500,1557-7295

Proyecto español: MTM2009-11686 ; MTM2012-34787

Url de la publicación: http://dx.doi.org/10.1145/2591004