LENGTH BIASED BETA-PARETO DISTRIBUTION AND ITS STRUCTURAL PROPERTIES WITH APPLICATION

Abstract

The concept of length biased distribution can be employed in development of proper models for lifetime data. Its method is adjusting the original probability density function from real data and the expectation of those data. This adjustment can bring about to correct conclusions of models. Therefore, we introduced the Length Biased Beta-Pareto (LBBP) distribution, so-called a new generalized of Pareto distribution in this article. The distribution is more flexible and has some interesting properties such as hazard rate, Renyi and Shannon entropies and other types of distribution. There are several sub-models include in the length biased Pareto, arcsine, log-beta, exponential and beta-Pareto distributions. We apply maximum likelihood estimation to estimate parameters of the distribution. We illustrate the superiority of the LBBP distribution to Norwegian fire claims data. The LBBP distribution seems to be the most appropriate model for this data set, since it provides a significantly better fit than the length biased Pareto and the beta-Pareto distributions. We hope that the LBBP distribution is an alternative distribution can be used in lifetime data analysis and other fields.