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Abstract
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This paper introduces a new four-parameter extension of the generalized Gompertz distributions. This distribution involves
some well-known distributions such as extension of generalized exponential, generalized exponential, and generalized Gompertz
distributions. In addition, it can have a decreasing, increasing, upside-down bathtub, and bathtub-shaped hazard rate function
depending on its parameters. Some mathematical properties of this new distribution, such as moments, quantiles, hazard rate
function, and reversible hazard rate function are obtained. In addition, the density function and the moments of the ordered
statistics of this new distribution is provided. The parameters of model are estimated using the maximum likelihood method.
Also, a real data set was used to illustrate the validity of the proposed distribution
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