SURVIVAL MODELS FOR HETEROGENEOUS POPULATIONS DERIVED FROM STABLE-DISTRIBUTIONS
SURVIVAL MODELS FOR HETEROGENEOUS POPULATIONS DERIVED FROM STABLE-DISTRIBUTIONS
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DOI：
10.1093/biomet/73.2.387
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发表时间：
1986-08-01
期刊：
影响因子：
2.7
通讯作者：
HOUGAARD, P
中科院分区：
文献类型：
--
作者：
HOUGAARD, P
提出了一个新的正数上的三参数分布族。它包括正数上的稳定分布、伽玛分布、退化分布和逆高斯分布。该族的特点是由拉普拉斯变换，从其中的时刻，卷积，无限可分性，单峰性和其他属性。密度是复杂的，但提供了一个简单的鞍点近似。威布尔分布和Gompertz分布在某些分布上是自然混合的。该族在其中一个参数上是自然指数的。该分布可作为脆弱性分布应用于异质种群的生命表方法中。这种分布的理想属性进行了讨论。例如，考虑心肌梗死后的存活率。
A new three-parameter family of distributions on the positive numbers is proposed. It includes the stable distributions on the positive numbers, the gamma, the degenerate and the inverse Gaussian distributions. The family is characterized by the Laplace transform, from which moments, convolutions, infinite divisibility, unimodality and other properties are derived. The density is complicated, but a simple saddlepoint approximation is provided. Weibull and Gompertz distributions are naturally mixed over some of the distributions. The family is natural exponential in one of the parameters. The distributions are relevant for application as frailty distributions in life table methods for heterogeneous populations. Desirable properties of such distributions are discussed. As an example survival after myocardial infarction is considered.