On sharp and highly manageable asymptotic approximations for instances of the Meijer G function

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Abstract

Instances of the Meijer G function may be used as representations for the probability density function (p.d.f.) and cumulative density function (c.d.f.) of several distributions. However, although the Meijer G function is a very handy representation for the p.d.f. and c.d.f. of these distributions, and nevertheless prominent progress has been made in its computation, this still remains very heavy, and time consuming, even with the newer versions of symbolic and extended precision softwares, so that the development of sharp and fast approximations is a desirable goal. In this paper it is shown how extremely sharp approximations for particular instances of the Meijer G function may be based on the probability density and cumulative distribution functions of the Generalized Near-Integer Gamma distribution.

Original languageEnglish
Title of host publicationProceedings of the International Conference on Numerical Analysis and Applied Mathematics 2014, ICNAAM 2014
PublisherAmerican Institute of Physics Inc.
Volume1648
ISBN (Electronic)978-0-7354-1287-3
DOIs
Publication statusPublished - 10 Mar 2015
EventInternational Conference on Numerical Analysis and Applied Mathematics 2014, ICNAAM 2014 - Rhodes, Greece
Duration: 22 Sep 201428 Sep 2014

Conference

ConferenceInternational Conference on Numerical Analysis and Applied Mathematics 2014, ICNAAM 2014
CountryGreece
CityRhodes
Period22/09/1428/09/14

Keywords

  • Characteristic function
  • Generalized near-integer gamma distribution
  • Inverse mellin transform
  • Mellin-barnes integral
  • Product of independent beta random variables
  • Sum of independent Logbeta random variables
  • BETA RANDOM-VARIABLES

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