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Distribution of a sum of weighted noncentral chi-square variables

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Abstract

We derive Laguerre expansions for the density and distribution functions of a sum of positive weighted noncentral chi-square variables. The procedure that we use is based on the inversion of Laplace transforms. The formulas so obtained depend on certain parameters, which adequately chosen will give some expansions already known in the literature and some new ones. We also derive precise bounds for the truncation error.

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Authors and Affiliations

  1. Departamento de Estadística e Investigación Operativa, Universidad de Cádiz, Spain

    Antonia Castaño-Martínez

  2. Departamento de Estadística e Investigación Operativa, Universidad de Sevilla, Spain

    Fernando López-Blázquez

Authors
  1. Antonia Castaño-Martínez
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  2. Fernando López-Blázquez
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Corresponding author

Correspondence to Antonia Castaño-Martínez.

Additional information

This research was partially supported by FQM-331, FQM-270, BMF 2001-2378 and BMF2002-04525-C02-02

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Castaño-Martínez, A., López-Blázquez, F. Distribution of a sum of weighted noncentral chi-square variables. TEST 14, 397–415 (2005). https://doi.org/10.1007/BF02595410

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  • DOI: https://doi.org/10.1007/BF02595410

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