Log-Weighted Pareto Distribution And Its Statistical Properties

Journal of Data Science

article

Rasha Mohamed Mandouh¹  Mahmoud Abdel-ghaffar Mohamed¹ 

[1] Department of Mathematical Statistics, Faculty of Graduate Studies for Statistical Research, Cairo University

关键词: Log-weighted Pareto distribution;    weighted distributions;    survival function;    hazard rate function;   

DOI  :  10.6339/JDS.202001_18(1).0009

学科分类：土木及结构工程学

来源: JDS

【 摘 要 】

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.

【 授权许可】

CC BY