Generalized Pareto distribution based on generalized order statistics and associated inference

Mansoor Rashid Malik; Devendra Kumar

doi:10.21307/stattrans-2019-024

Generalized Pareto distribution based on generalized order statistics and associated inference

Mansoor Rashid Malik , Devendra Kumar Department of Statistics, Central University of Haryana, Mahendergarh, India ORCID:https://orcid.org/0000-0001-5831-3315 Statistics in Transition new series, vol. 20, 2019, 3, pages: 57-79 Published online: 30 August 2019 DOI 10.21307/stattrans-2019-024

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ABSTRACT

In this paper, we have considered the generalized Pareto distribution. Various structural properties of the distribution are derived including (quantile function, explicit expressions for moments, mean deviation, Bonferroni and Lorenz curves and Renyi entropy). We have provided simple explicit expressions and recurrence relations for single and product moments of generalized order statistics from the generalized Pareto distribution. The method of maximum likelihood is adopted for estimating the model parameters. For different parameter settings and sample sizes, the simulation studies are performed and compared to the performance of the generalized Pareto distribution.

KEYWORDS

generalized order statistics, generalized Pareto distribution, single and product moment, recurrence relations, characterization and maximum likelihood estimation

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