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In addition to the generalized families of distributions mentioned earlier, there are several other generalized families of distributions in the literature and these are contained in Owoloko et al. Besides, estimation of the parameters of Lomax distribution under general progressive censoring has also been considered by Al-Zahrani and Al-Sobhi.
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Modified and extended versions of the Lomax distribution have been studied examples include the weighted Lomax distribution, exponential Lomax distribution, exponentiated Lomax distribution, gamma Lomax distribution, transmuted Lomax distribution, Poisson Lomax distribution, McDonald Lomax distribution, Weibull Lomax distribution, and power Lomax distribution. It has also been considered to be useful in reliability and life testing problems in engineering and in survival analysis as an alternative distribution. The distribution was defined by Lomax and it is a heavy-tailed distribution. The Lomax distribution can also be called Pareto Type II distribution and its application can be found in many fields like actuarial science, economics, and so on. Excerpt from the analysis indicates that the Gompertz Lomax distribution performed better than the Beta Lomax distribution, Weibull Lomax distribution, and Kumaraswamy Lomax distribution. A simulation study to assess the performance of the parameters of Gompertz Lomax distribution was provided and an application to real life data was provided to assess the potentials of the newly derived distribution. In this present study, the Lomax distribution was extended using the Gompertz family of distribution, its resulting densities and statistical properties were carefully derived, and the method of maximum likelihood estimation was proposed in estimating the model parameters. Developing new compound distributions which are more flexible than the existing distributions have become the new trend in distribution theory.