The beta length-biased Pareto distribution with an application for Norwegian fire claims

摘要

In this article, a new four-parameter beta length-biased Pareto distribution is developed and studied. Various properties of this distribution are discussed. The new distribution has either a unimodal or a decreasing hazard rate. The expressions for the mean, mean deviation, variance, skewness, kurtosis and Renyi and Shannon entropies are obtained. The relationship between these moments and the parameters are presented. The method of maximum likelihood is proposed to estimate the parameters of the distribution. Finally, the new distribution is applied to Norwegian fire claims data.