A New Probability Distribution for Modeling Failure and Service Times: Properties, Copulas and Various Estimation Methods

Hanaa Elgohari,Mohamed Ibrahim,Haitham Yousof

doi:10.19139/soic-2310-5070-1101

Abstract

In this paper, a new generalization of the Pareto type II model is introduced and studied. The new density canbe “right skewed” with heavy tail shape and its corresponding failure rate can be “J-shape”, “decreasing” and “upside down (or increasing-constant-decreasing)”. The new model may be used as an “under-dispersed” and “over-dispersed” model. Bayesian and non-Bayesian estimation methods are considered. We assessed the performance of all methods via simulation study. Bayesian and non-Bayesian estimation methods are compared in modeling real data via two applications. In modeling real data, the maximum likelihood method is the best estimation method. So, we used it in comparing competitive models. Before using the the maximum likelihood method, we performed simulation experiments to assess the finite sample behavior of it using the biases and mean squared errors.

Highlights

The Pareto type II distribution is a heavy-tail probability distribution used in business, actuarial science, biological sciences, engineering, economics, income and wealth inequality, queueing theory, size of cities, and Internet traffic modeling
The main aim of this work is to provide a flexible extension of the Pareto type II distribution using the odd BurrG (OB-G) family defined by Alizadeh et al [6]
The major motivation for the practicality of the odd Burr Pareto type II (OBP) model is based on the wider importance of the standard Pareto type II model

Summary

Introduction

The Pareto type II ( called as Lomax) distribution is a heavy-tail probability distribution used in business, actuarial science, biological sciences, engineering, economics, income and wealth inequality, queueing theory, size of cities, and Internet traffic modeling (see Lomax [41]). The Pareto type II model is known as a special model form of Pearson type VI distribution and has considered as a mixture of exponential (Exp) and gamma (Gam) distributions. The Pareto type II distribution has been suggested as heavy tailed alternative to the Exp, Weibull (W) and Gam distributions (Bryson [20]). For details about relation between the Pareto type II model and the Burr family and Compound Gamma (CGam) model see Tadikamalla [62] and Durbey [24]

Objectives

Methods

Conclusion