Journal of Data Science

bstract: In this article we propose further extension of the generalized Marshall Olkin-G ( GMO - G ) family of distribution. The density and survival functions are expressed as infinite mixture of the GMO - G distribution. Asymptotes, Rényi entropy, order statistics, probability weighted moments, moment generating function, quantile function, median, random sample generation and parameter estimation are investigated. Selected distributions from the proposed family are compared with those from four sub models of the family as well as with some other recently proposed models by considering real life data fitting applications. In all cases the distributions from the proposed family out on top.

Abstract: A family of distribution is proposed by using Kumaraswamy-G ( Kw − G ) distribution as the base line distribution in the generalized Marshall-Olkin (GMO) construction. By expanding the probability density function and the survival function as infinite series the proposed family is seen as infinite mixtures of the Kw − G distribution. Series expansions of the density function for order statistics are also obtained. Moments, moment generating function, Rényi entropy, quantile function, random sample generation, asymptotes, shapes and stochastic orderings are also investigated. Maximum likelihood estimation, their large sample standard error, confidence intervals and method of moment are presented. Three real life illustrations of comparative data modeling applications with some of the important sub mode

This paper presents a new generalization of the extended Gompertz distribution. We defined the so-called exponentiated generalized extended Gompertz distribution, which has at least three important advantages: (i) Includes the exponential, Gompertz, extended exponential and extended Gompertz distributions as special cases; (ii) adds two parameters to the base distribution, but does not use any complicated functions to that end; and (iii) its hazard function includes inverted bathtub and bathtub shapes, which are particularly important because of its broad applicability in real-life situations. The work derives several mathematical properties for the new model and discusses a maximum likelihood estimation method. For the main formulas related to our model, we present numerical studies that demonstrate 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 EGEG model. Three real- world data sets were used for applications in order to illustrate the usefulness of our proposal.