Functional equations involving Sibuya’s dependence function
Aequationes mathematicae(2018)
摘要
We introduce a new probability aging notion via a functional equation based on the tail invariance of Sibuya’s dependence function which is specified as the ratio between the joint survival function and the product of its marginal survival functions. Solutions of the functional equation are generated by Gumbel’s type I bivariate exponential distribution and independence law. In a particular setting, we construct a version of Gumbel’s law with a singular component.
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关键词
Bivariate lack of memory property,Characterization,Copula,Dependence function,Functional equations,Gumbel’s type I bivariate exponential distribution,Hazard rate,Marshall–Olkin’s fatal shock model
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