A New Gumbel Generated Family of Distributions: Properties, Bivariate Distribution and Application

Elebe E. Nwezza^1, , Chinonyerem V. Ogbuehi², Uchenna U. Uwadi¹ and C.O. Omekara²

¹Department of Mathematics/Computer Science/Statistics/Informatics, Alex Ekwueme Federal University Ndufu alike, Ikwo, Nigeria

²Department of Statistics, Micheal Okpara University of Agriculture, Umudike, Nigeria

Cite this paper

Elebe E. Nwezza, Chinonyerem V. Ogbuehi, Uchenna U. Uwadi and C.O. Omekara. A New Gumbel Generated Family of Distributions: Properties, Bivariate Distribution and Application. American Journal of Applied Mathematics and Statistics. 2020; 8(1):9-20. doi: 10.12691/AJAMS-8-1-2

Abstract

In this paper, we propose a new class of Gumbel generated distributions called Gumbel-Marshall-Olkin family of distributions. The new family of distributions is represented as linear mixture of exponentiated-G distribution. Some of the sub-models are presented. We derived some characterizations such as the quantile, moments, moment generating function, entropy and order statistics of the proposed family of distributions. The estimation of the unknown parameters of the new class of distribution is through the maximum likelihood. The consistency of the MLEs of the sub-model is assessed by means of simulation. Furthermore, we derive the bivariate density function of the new class of distributions. Two real life data sets are used to illustrate the potential usefulness of the sub-models of the proposed class of distributions. The results of the applications clearly indicate that the sub-models of the proposed class of distribution provided better fit among the other competing models.

Keywords

Gumbel distribution, Marshall-Olkin distribution, Bivariate distribution, Moment, Maximum Likelihood

Copyright

This work is licensed under a Creative Commons Attribution 4.0 International License. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/

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