Marshall-Olkin扩展重尾分布的刻画

Characterizations on Marshall-Olkin Extended Heavy-tailed Distribution

利用Marshall-Olkin提出构造分布的方法,以重尾分布F作为基础,提出了Marshall-Olkin扩展重尾分布G,根据常见重尾分布子族的定义及其等价关系,分析了F与G的相关性质,对于重尾分布族,G具有封闭性,尾等价性,同时在连续型分布情形下,讨论了F与G的密度函数之间及风险率函数之间的关系.最后,将Marshall-Olkin扩展重尾分布应用于实际数据中,并在拟合数据方面与原分布进行比较,表明扩展分布要优于原分布.

Marshall and Olkin proposed a new method to estabilish new families of distributions by adding a parameter to a distribution.In this paper,based on heavy-tailed distribution F,Marshall-Olkin extended heavy-tailed distribution G is introduced.Properties related to Marshall-Olkin extended heavy-tailed distribution are discussed according to the definitions and the equivalent conditions of common subclasses of heavy-tailed distribution.It is concluded that Marshall-Olkin extended heavy-tailed distribution G has the properties of closure and tail equivalence for classes of heavy-tailed distribution.At the same time,this paper investigates not only the relation of the density function of F and G but also the hazard rate function in the continuous distribution.Finally,a real data is used to compare the Marshall-Olkin extended heavy-tailed distribution with original distribution in term of model fitting.It is shown that extended distribution is better than original distribution.