Some Normal Approximations for Renewal Function of Large Weibull Shape Parameter
Some Normal Approximations for Renewal Function of Large Weibull Shape Parameter
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DOI：
10.1081/sac-120013107
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发表时间：
2003-01
期刊：
影响因子：
--
通讯作者：
L. Cui;M. Xie
中科院分区：
文献类型：
--
作者：
L. Cui;M. Xie
由于威布尔分布以一种相对简单的解析方式描述了广泛的现实行为，并且其形状和尺度参数可以很容易地用图形或统计方法来确定，因此威布尔更新函数引起了人们的极大关注。另一方面，除了指数分布的特殊情况外，威布尔更新函数没有闭合形式的解析解。通常使用边界、近似值和表。本文研究了基于威布尔分布正态逼近的几种逼近方法。与已有文献不同的是，当形状参数为中、大尺寸时，这种方法对威布尔更新函数是有利的。还可以得到级数截断表达式和近似界。文中给出了数值算例和比较，以说明该方法的有效性。
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.