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A new mixture Pareto distribution and its application. (English) Zbl 1365.60008

Summary: This paper introduces a new mixture Pareto distribution generated from logit of the weighted two-component mixture distribution which is mixed between a Pareto and a length biased Pareto distributions. Special sub-models include the Pareto, exponential, chi-square and logistic distributions. We contain derivation of the mixture Pareto types II, III, IV and provide various mathematical properties including its limit behavior, hazard rate and \(r\)-th moment. Discussion of the estimation procedure is based on maximum likelihood. Also, we display an application to Norwegian fire claim data, it shows that the mixture Pareto distribution give a better fit than other important lifetime models; a Weibull, the Pareto and the length biased Pareto distributions. In conclusion, the mixture Pareto distribution provides a rather general and flexible framework for the statistical lifetime data analysis.

MSC:

60E05 Probability distributions: general theory
62N05 Reliability and life testing
62P05 Applications of statistics to actuarial sciences and financial mathematics