Flexibility of Generalized Distributions
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Date
2022-09-12
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Royal Statistical Society Nigeria Local Group
Abstract
Some existing distributions are limited in shapes of Probability Density Function (PDF) and Hazard Function (HF) which constrains their use in analysis of certain types of data. Generalizing these distributions often deal with this constraints on usage by introducing flexibility. Generalized distributions were derived using the Generalized Pareto Distribution (GPD) as base distribution. Exponentiated GPDs called Lehmann Type II GPD (LIIGPD) and Lehmann Type I GPD (LIGPD) having an additional parameter each were obtained by applying Lehmann Alternative 1 (LA1) and Lehmann Alternative 2 (LA2) parameter induction methods respectively. Flexibility of generalized distributions was established by comparing the shapes of probability density and hazard functions of LIIGPD and LIGPD with those of the GPD. No new probability density or hazard shape was introduced by LIIGPD but the new shape introduced by LIGPD demonstrated flexibility of generalized distributions. Generalized distributions do not always introduce new density and hazard shapes but often improve flexibility of distributions.
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Keywords
Generalized distributions; Flexibility, Generalized Pareto Distribution; Probability Density Function; Hazard Function; Lehmann Alternative 1; Lehmann Alternative 2.
Citation
Omekam, I. V. and Adejumo, A. O. (2022). Flexibility of Generalized Distributions. RSS-NLG 2021 Conference Proceedings, Olayiwola O.M. (ed.) 168-181. Published by Royal Statistical Society Nigeria Local Group.