A comparison of the generalized gamma and exponentiated Weibull distributions
A comparison of the generalized gamma and exponentiated Weibull distributions
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DOI：
10.1002/sim.6159
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发表时间：
2014-09-20
影响因子：
2
通讯作者：
Matheson, Matthew
中科院分区：
文献类型：
--
作者：
Cox, Christopher;Matheson, Matthew
本文对三参数指数威布尔 (EW) 分布和广义伽玛 (GG) 分布进行了比较。这两个不同家族之间的联系在于，两者的危险函数都具有四种标准形状（递增、递减、浴缸和弧形），并且事实上，对于三个参数相同的值，危险的形状是相同的。对于给定的 EW 分布，我们使用模拟以及匹配第 5 个、第 50 个和第 95 个百分位数来定义匹配 GG。我们使用 Kullback-Leibler 距离以图形方式比较 EW 和匹配 GG 分布。我们发现 EW 和匹配 GG 的生存函数在图形上无法区分，只有危险函数有时可以看出略有不同。 Kullback-Leibler 距离非常小，并且随着样本量的增加而减小。我们得出的结论是，这两个分布之间的相似性是惊人的，因此，EW 是 GG 的一个方便的替代方案，具有相同丰富的危险行为。更重要的是，这些结果表明，四种基本危险形状在某种程度上可能是任何分布族的重要结构特征。版权所有 (c) 2014 约翰·威利父子有限公司
This paper provides a comparison of the three-parameter exponentiated Weibull (EW) and generalized gamma (GG) distributions. The connection between these two different families is that the hazard functions of both have the four standard shapes (increasing, decreasing, bathtub, and arc shaped), and in fact, the shape of the hazard is the same for identical values of the three parameters. For a given EW distribution, we define a matching GG using simulation and also by matching the 5 th, 50 th, and 95 th percentiles. We compare EW and matching GG distributions graphically and using the Kullback-Leibler distance. We find that the survival functions for the EW and matching GG are graphically indistinguishable, and only the hazard functions can sometimes be seen to be slightly different. The Kullback-Leibler distances are very small and decrease with increasing sample size. We conclude that the similarity between the two distributions is striking, and therefore, the EW represents a convenient alternative to the GG with the identical richness of hazard behavior. More importantly, these results suggest that having the four basic hazard shapes may to some extent be an important structural characteristic of any family of distributions. Copyright (c) 2014 John Wiley & Sons, Ltd.