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The beta generalized Pareto distribution with application to lifetime data. (English) Zbl 1219.62024
Summary: The generalized Pareto (GP) distribution is useful in modeling extreme value data, because of its long tail feature. In this paper, a new generalized version of this distribution which is called the beta generalized Pareto (BGP) distribution is introduced. The new distribution is more flexible and has some interesting properties. A comprehensive mathematical treatment of the BGP distribution is provided. We give closed-form expressions for the density, cumulative distribution and hazard rate function. We derive the \(r\) th raw moment of this distribution. Moreover, we discuss estimation by maximum likelihood and obtain an expression for Fisher’s information matrix. In the end, an application using three real data sets is presented.

MSC:
62E10 Characterization and structure theory of statistical distributions
62G32 Statistics of extreme values; tail inference
62N05 Reliability and life testing
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