A New Mixture Pareto Distribution and Its Application

Abstract

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 I,II , III and IV provide various mathematical properties including its limit behavior, hazard rate and  rth 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.