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The Gompertz Gumbel II Distribution: Properties and Applications

Adebisi Ade Ogunde, Gbenga Adelekan Olalude and Donatus Osaretin Omosigho
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Adebisi Ade Ogunde: Department of Statistics, University of Ibadan, Oyo State, Nigeria
Gbenga Adelekan Olalude: Department of Statistics, Federal Polytechnic Ede, Osun State, Nigeria
Donatus Osaretin Omosigho: Department of Mathematics and Statistics, Federal Polytechnic Ado-Ekiti, Ekiti State, Nigeria

Academic Journal of Applied Mathematical Sciences, 2021, vol. 7, issue 1, 1-15

Abstract: In this paper we introduced Gompertz Gumbel II (GG II) distribution which generalizes the Gumbel II distribution. The new distribution is a flexible exponential type distribution which can be used in modeling real life data with varying degree of asymmetry. Unlike the Gumbel II distribution which exhibits a monotone decreasing failure rate, the new distribution is useful for modeling unimodal (Bathtub-shaped) failure rates which sometimes characterised the real life data. Structural properties of the new distribution namely, density function, hazard function, moments, quantile function, moment generating function, orders statistics, Stochastic Ordering, Renyi entropy were obtained. For the main formulas related to our model, we present numerical studies that illustrate the practicality of computational implementation using statistical software. We also present a Monte Carlo simulation study to evaluate the performance of the maximum likelihood estimators for the GGTT model. Three life data sets were used for applications in order to illustrate the flexibility of the new model.

Keywords: Quantile function; Bathtub-shaped failure rate; Renyl entropy; Orders statistics. (search for similar items in EconPapers)
Date: 2021
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