The Weibull renewal function for moderate to large arguments

A. G. Constantine; N. I. Robinson

doi:10.1016/S0167-9473(96)00052-7

The Weibull renewal function for moderate to large arguments

A. G. Constantine
, N. I. Robinson

Research output: Contribution to journal › Article › peer-review

31 Citations (Scopus)

Abstract

Damped exponential series are developed for the Weibull renewal function, with shape parameter m > 1, by residue calculations of the Laplace transformation of the renewal integral equation. Asymptotic properties of the Laplace transform of the Weibull distribution, a Faxen integral, are used to determine both the residues and prove series convergence. This new series fills the void between the existing power series of the renewal function, useful for small arguments and also for m ≤ 1, and the known asymptotic behaviour.

Original language	English
Pages (from-to)	9-27
Number of pages	19
Journal	Computational Statistics and Data Analysis
Volume	24
Issue number	1
DOIs	https://doi.org/10.1016/S0167-9473(96)00052-7
Publication status	Published - 6 Mar 1997
Externally published	Yes

Keywords

Asymptotic expansions
Faxen's integral
Laplace transform
Renewal function
Weibull distribution
Zero calculations

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AU - Robinson, N. I.

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AB - Damped exponential series are developed for the Weibull renewal function, with shape parameter m > 1, by residue calculations of the Laplace transformation of the renewal integral equation. Asymptotic properties of the Laplace transform of the Weibull distribution, a Faxen integral, are used to determine both the residues and prove series convergence. This new series fills the void between the existing power series of the renewal function, useful for small arguments and also for m ≤ 1, and the known asymptotic behaviour.

KW - Asymptotic expansions

KW - Faxen's integral

KW - Laplace transform

KW - Renewal function

KW - Weibull distribution

KW - Zero calculations

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JF - Computational Statistics and Data Analysis

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ER -

The Weibull renewal function for moderate to large arguments

Abstract

Keywords

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