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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
Ghitany et al. (Tue,) studied this question.
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