The Complementary Geometric Topp–Leone‐G Family of Distributions With Applications to Insurance and Engineering Data

In this article, we study and discuss a new family of distributions called the complementary geometric Topp–Leone generated family of distributions. Some statistical and mathematical properties of the complementary geometric Topp–Leone generated family are computed. Three submodels of the new suggested family, such as the complementary geometric Topp–Leone exponential distribution, the complementary geometric Topp–Leone Rayleigh distribution, and the complementary geometric Topp–Leone Lomax distribution, are discussed. The method of maximum likelihood is used to estimate the parameters of the complementary geometric Topp–Leone‐generated family. A simulation study is conducted for the complementary geometric Topp–Leone exponential distribution as a submodel of the suggested family. Finally, we illustrate the complementary geometric Topp–Leone exponential distribution as a submodel of the suggested family with three real applications, and we compared it to seven well‐known statistical models, such as the Topp–Leone exponential distribution, the Topp–Leone exponentiated exponential distribution, the exponentiated generalized Topp–Leone exponential distribution, the exponentiated Lomax distribution, the Weibull Lomax distribution, exponentiated Weibull Lomax distribution, and the exponential distribution. It shows that the new family is appropriate and has potential for a lifetime analysis.