Marshall–Olkin Extended Lomax Distribution and Its Application to Censored Data

TLDR

The paper studies a new parametric distribution derived from the Marshall–Olkin extension of the Lomax model. The authors fit the new distribution to randomly censored data using maximum likelihood estimation. The distribution is a compound exponential mixture, its density and hazard rate shapes satisfy simple sufficient conditions, and its sample extreme limits are exponential and Fréchet. Keywords include compound distribution, extreme order statistics, hazard rate, Kaplan–Meier estimator, likelihood ratio test, and the MSC codes are 62N01, 62N02, 62N03, 62N05, 60E15.

Abstract

Abstract This paper investigates properties of a new parametric distribution generated by Marshall and Olkin (Citation1997) extended family of distributions based on the Lomax model. We show that the proposed distribution can be expressed as a compound distribution with mixing exponential model. Simple sufficient conditions for the shape behavior of the density and hazard rate functions are given. The limiting distributions of the sample extremes are shown to be of the exponential and Fréchet type. Finally, utilizing maximum likelihood estimation, the proposed distribution is fitted to randomly censored data. Keywords: Compound distributionExtreme order statisticsGeometric extreme stabilityHazard rateKaplan–Meier estimatorLikelihood ratio testLimiting distributionLomax distributionMaximum likelihoodP–P plotMathematics Subject Classification: Primary 62N01, 62N02, 62N03, 62N05Secondary 60E15