文章基本信息

标题：A method of moments to estimate bivariate survival functions: the copula approach
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作者：Silvia Angela Osmetti ; Paola Maddalena Chiodini
期刊名称：Statistica
印刷版ISSN：1973-2201
出版年度：2011
卷号：71
期号：4
页码：469-488
DOI：10.6092/issn.1973-2201/3628
语种：English
出版社：Dep. of Statistical Sciences "Paolo Fortunati", Università di Bologna
摘要：In this paper we discuss the problem on parametric and non parametric estimation of the distributions generated by the Marshall-Olkin copula. This copula comes from the Marshall-Olkin bivariate exponential distribution used in reliability analysis. We generalize this model by the copula and different marginal distributions to construct several bivariate survival functions. The cumulative distribution functions are not absolutely continuous and they unknown parameters are often not be obtained in explicit form. In order to estimate the parameters we propose an easy procedure based on the moments. This method consist in two steps: in the first step we estimate only the parameters of marginal distributions and in the second step we estimate only the copula parameter. This procedure can be used to estimate the parameters of complex survival functions in which it is difficult to find an explicit expression of the mixed moments. Moreover it is preferred to the maximum likelihood one for its simplex mathematic form; in particular for distributions whose maximum likelihood parameters estimators can not be obtained in explicit form.