The beta generalized Gompertz distribution |
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Institution: | 1. Laboratory of Applied Mathematics, Mohamed Khider University, Biskra, 07000, Algeria;2. Department of Mathematics and Informatics, Larbi Ben M’Hidi University, Oum El Bouaghi, 04000, Algeria |
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Abstract: | A new five-parameter continuous model called the beta generalized Gompertz distribution is introduced and studied. This distribution contains the Gompertz, generalized Gompertz, beta Gompertz, generalized exponential, beta generalized exponential, exponential and beta exponential distributions as special sub-models. Some mathematical properties of the new model are derived. We show that the density function of the new distribution can be expressed as a linear combination of Gompertz densities. We obtain explicit expressions for the moments, moment generating function, quantile function, density function of the order statistics and their moments, mean deviations, Bonferroni and Lorenz curves and Rényi entropy. The model parameters are estimated by using the maximum likelihood method of estimation and the observed information matrix is determined. Finally, an application to real data set is given to illustrate the usefulness of the proposed model. |
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