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Monotonicity properties and bounds for the chi-square and gamma distributions.

Abstract: The generalized Marcum functions Qlðx; yÞ and Plðx; yÞ have as particular cases the noncentral 2 and gamma cumulative distributions, which become central distributions (incomplete gamma function ratios) when the non-centrality parameter x is set to zero. We analyze monotonicity and convexity properties for the generalized Marcum functions and for ratios of Marcum functions of consecutive parameters (differing in one unity) and we obtain upper and lower bounds for the Marcum functions. These bounds are proven to be sharper than previous estimations for a wide range of the parameters. Additionally we show how to build convergent sequences of upper and lower bounds. The particularization to incomplete gamma functions, together with some additional bounds obtained for this particular case, lead to combined bounds which improve previously existing inequalities.

 Fuente: Applied Mathematics and Computation, 2014, 246, 399-415

Editorial: Elsevier

 Año de publicación: 2014

Nº de páginas: 16

Tipo de publicación: Artículo de Revista

 DOI: 10.1016/j.amc.2014.08.034

ISSN: 0096-3003,1873-5649

Proyecto español: MTM2012-34787

Url de la publicación: http://dx.doi.org/10.1016/j.amc.2014.08.034