Count Distribution for Generalized Weibull Duration with Applications

被引：5
|
作者：
Ong, S. H. [1 ]
Biswas, Atanu [2 ]
Peiris, S. [3 ]
Low, Y. C. [1 ]
机构：
[1] Univ Malaya, Inst Math Sci, Kuala Lumpur 50603, Malaysia
[2] Indian Stat Inst, Appl Stat Unit, Kolkata, India
[3] Univ Sydney, Sch Math & Stat, Sydney, NSW 2006, Australia
来源：
COMMUNICATIONS IN STATISTICS-THEORY AND METHODS | 2015年 / 44卷 / 19期
关键词：
Birth and renewal processes; Inter arrival times; Gamma distribution; Poisson distribution; Renewal function; Over and under dispersion; Laplace transform; Parameter estimation; Goodness-of-fit; Likelihood ratio test; RENEWAL FUNCTION; SERIES; MODELS;
D O I：
10.1080/03610926.2015.1062105
中图分类号：
O21 [概率论与数理统计]; C8 [统计学];
学科分类号：
020208 ; 070103 ; 0714 ;
摘要：
An extension of the Poisson distribution is derived by considering a stochastic point process where the duration has a generalized Weibull distribution. This distribution is able to represent under, equi and over dispersion, a useful feature in data analysis. The computation of the probabilities and renewal function (expected number of renewals) are examined. Parameter estimation by the method of maximum likelihood is considered with applications of the count distribution to real frequency count data exhibiting under and over dispersion. It is shown that the generalized Weibull count distribution fits much better than the Weibull and gamma duration models.
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页码：4203 / 4216
页数：14
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