Please use this identifier to cite or link to this item: https://doi.org/10.1081/SAC-120013107
Title: Some normal approximations for renewal function of large Weibull shape parameter
Authors: Cui, L. 
Xie, M. 
Keywords: Normal approximation
Renewal function
Series truncation approximation
Shape parameter
Weibull distribution
Issue Date: Feb-2003
Citation: Cui, L., Xie, M. (2003-02). Some normal approximations for renewal function of large Weibull shape parameter. Communications in Statistics Part B: Simulation and Computation 32 (1) : 1-16. ScholarBank@NUS Repository. https://doi.org/10.1081/SAC-120013107
Abstract: Weibull renewal function has attracted a lot of attention because the Weibull distribution describes in a relatively simple analytical manner a wide range of realistic behavior and its shape and scale parameters can be readily determined with graphical or statistical procedure. On the other hand, there are no closed form analytical solutions for the Weibull renewal function except for the special case of exponential distribution. Bounds, approximations, and tables are usually used. In this article, some approximations based on Normal approximation of Weibull distribution are studied. Such a procedure, which is different from that in the existing literature, is shown to be good for Weibull renewal function when the shape parameter is of moderate or large size. Series truncation expression and approximation bounds can be obtained as well. Numerical examples and comparisons are shown to illustrate the procedure.
Source Title: Communications in Statistics Part B: Simulation and Computation
URI: http://scholarbank.nus.edu.sg/handle/10635/63331
ISSN: 03610918
DOI: 10.1081/SAC-120013107
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