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Abstract
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A new extension of the Topp-Leone distribution is developed to produce a new family of distributions, namely Topp-Leone Gompertz-G distribution. Some of its structural properties including expansion of density, distribution of order statistics, Renyi entropy, moments, quantile, and generating functions are derived. We considered four special cases of the new distribution and we conclude that the distribution can handle heavy tailed data and non-monotonic hazard rate functions. A simulation study was conducted to examine the performance of the special case of the proposed family of distributions. Two lifetime data examples are included in this article to illustrate the applicability of the proposed model in comparison with other competing non-nested models.
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