On certain countable mixtures of absolutely continuous distributions

摘要

Countable mixtures with Pascal (r, p) mixing proportions and positive integer powers of the survival function of an absolutely continuous distribution F produce anew class of distributions, denoted by T~*(Pascal(r, p), F). A member of this class has two extra parameters (r, p) than the original distribution. This makes such a member richer and more flexible for modeling continuous type data. Members of class T~*(Pascal(r, p), F) have been characterized, their failure rate functions studied and the life of a k-out-of-n structure obtained. An illustrative example is given when F is the survival function of the Weibull distribution.