The Weibull renewal function for moderate to large arguments

被引：23

作者：

Constantine, AG ^{[1
]}

Robinson, NI ^{[1
]}

机构：

[1] CSIRO,DIV MATH & STAT,URRBRAE,SA 5064,AUSTRALIA

来源：

COMPUTATIONAL STATISTICS & DATA ANALYSIS | 1997年 / 24卷 / 01期

关键词：

Weibull distribution; renewal function; Laplace transform; Faxen's integral; asymptotic expansions; zero calculations;

D O I：

10.1016/S0167-9473(96)00052-7

中图分类号：

TP39 [计算机的应用];

学科分类号：

081203 ; 0835 ;

摘要：

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 less than or equal to 1, and the known asymptotic behaviour.

引用

页码：9 / 27

页数：19

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