Log-Weighted Pareto Distribution And Its Statistical Properties

Abstract

The Pareto distribution is a power law probability distribution that is used to describe social scientific, geophysical, actuarial, and many other types of observable phenomena. A new weighted Pareto distribution is proposed using a logarithmic weight function. Several statistical properties of the weighted Pareto distribution are studied and derived including cumulative distribution function, location measures such as mode, median and mean, reliability measures such as reliability function, hazard and reversed hazard functions and the mean residual life, moments, shape indices such as skewness and kurtosis coefficients and order statistics. A parametric estimation is performed to obtain estimators for the distribution parameters using three different estimation methods the maximum likelihood method, the L-moments method and the method of moments. Numerical simulation is carried out to validate the robustness of the proposed distribution. The distribution is fitted to a real data set to show its importance in real life applications.

New Odoma Distribution with Application to Cancer Data

“…The Odoma distribution is commenly used in fields of behavioral and emotional sciences. Odoma distribution to get some new distributions such as (7) proposed a new extension of Odoma distribution known as weighted Odoma distribution and discussed its properties and applications. (8) introduced Odoma distribution with various statistical properties and its application.…”