FLEXIBILITY OF GENERALIZED DISTRIBUTIONS

Ifeyinwa Vivian Omekam; Adebowale Olushola Adejumo

Ifeyinwa Vivian Omekam Faculty of Physical Sciences, University of Ilorin, Ilorin
Adebowale Olushola Adejumo Faculty of Physical Sciences, University of Ilorin, Ilorin, Nigeria

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.

Author Biographies

Ifeyinwa Vivian Omekam, Faculty of Physical Sciences, University of Ilorin, Ilorin

Department of Statistics,

Adebowale Olushola Adejumo, Faculty of Physical Sciences, University of Ilorin, Ilorin, Nigeria

Department of Statistics,