Residue series for the generalised gamma renewal function (Q2738638)
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scientific article; zbMATH DE number 1639775
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Residue series for the generalised gamma renewal function |
scientific article; zbMATH DE number 1639775 |
Statements
22 November 2001
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renewal function
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convolution series
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residue series
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Faxen's integral
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generalised gamma density function
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0.86942726
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0.8680587
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0.86577505
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0.86351055
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0.8591006
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0.8586179
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0.8543674
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Residue series for the generalised gamma renewal function (English)
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Asymptotic expansions for large values of time exist for commonly used probability density functions (pdfs), and to obtain small time renewal function convolution series are available for many of these pdfs. Although, in general, to obtain accurate medium time renewal function the numerical method is used in solving the renewal equation, in the case of Weibull pdf and certain gamma pdfs, the residue series obtained from the Laplace transform of the renewal equation is employed. The author discusses the formation and limitations of the convolution and residue series of the renewal function for the generalised gamma pdf, a pdf which encompasses both the Weibull and gamma pdfs.NEWLINENEWLINEFor the entire collection see [Zbl 0963.00027].
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