The Marshall-Olkin extended generalized Gompertz distribution

Abstract

A new four-parameter model called the Marshall-Olkin extended generalized Gompertz distribution is introduced. Its hazard rate function can be constant, increasing, decreasing, upside-down bathtub or bathtub-shaped depending on its parameters. Some mathematical properties of this model such as expansion for the density function, moments, moment generating function, quantile function, mean deviations, mean residual life, order statistics and Rényi entropy are derived. The maximum likelihood technique is used to estimate the unknown model parameters and the observed information matrix is determined. The applicability of the proposed model is shown by means of a real data set.

On Generalisation of Gompertz-Makeham Distribution

“…Many authors used the exponentiated class of distributions to derive a new class of distributions. Mudholkar & Srivastava (1993) and also Ahuja & Nash (1967) used the exponentiated class of distribution to derive exponentiated weibull distribution; Gupta & Kundu (2001) generalised the Exponential distribution to obtain exponentiated exponential; Anake et al (2015); Lemonte & Cordeiro (2011) and Benkhelifa (2017) presented the exponentiated generalized inverse gaussian, fractional beta-exponential and Marshall-Olkin extended generalized Gompertz-Makeham distribution respectively. The cdf of the exponentiated distribution is given accordingly as:…”