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An Application of the Residue Calculus: The Distribution of the Sum of Nonhomogeneous Gamma Variates.

The application of the calculus of residues in the computation of the nongamma probability density function for the sum of gamma variates with different shape parameters is discussed. The tool is used together with the inversion formula for characteristic functions for computing the distribution of...

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Published in:American Statistician Vol. 63; no. 1; pp. 37 - 40
Main Author: Hagwood, Charles
Format: Article
Published: American Statistical Association February 2009
Subjects:
Congruences & residues
Distribution (Probability theory)
Online Access:View this record in EBSCOhost
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      dt: February 2009
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      pub: American Statistical Association
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        10.1198/tast.2009.0007
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        atl: An Application of the Residue Calculus: The Distribution of the Sum of Nonhomogeneous Gamma Variates.
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        au: Hagwood, Charles
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        Congruences & residues
        Distribution (Probability theory)
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          Congruences & residues
          Distribution (Probability theory)
      ab: The application of the calculus of residues in the computation of the nongamma probability density function for the sum of gamma variates with different shape parameters is discussed. The tool is used together with the inversion formula for characteristic functions for computing the distribution of the sum of gamma variates, which is needed when solving problems in statistical inference as well as stochastic processes. Compared to previous methods for obtaining the density function of such a sum, this derivation appears to be more elegant. Moreover, the numerical computation is proven to be simple, especially in any symbolic computer language.
      pubtype: Academic Journal
      doctype: Article
      src: R
    language: English
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