The purpose of this paper is to introduce and study a new generated family of distributions based on the type II transformation which is called the type II exponentiated half-logistic-Gompertz-Topp-Leone-G (TIIEHL-Gom-TL-G) family of distributions. We investigate its general mathematical properties, including, hazard rate function, quantile function, moments, moment generating function, Rényi entropy and order statistics. Parameter estimates of the new family of distributions are obtained based on the maximum likelihood estimation method and their performance is evaluated via a simulation study. For illustration of the applicability of the new family of distributions, four real data sets are analyzed.

We develop and study in detail a new family of distributions called Half-logistic Odd Power Generalized Weibull-G (HLOPGW-G) distribution, which is a linear combination of the exponentiated-G family of distributions. From the special cases considered, the model can fit heavy tailed data and has non-monotonic hazard rate functions. We further assess and demonstrate the performance of this family of distributions via simulation experiments. Real data examples are given to demonstrate the applicability of the proposed model compared to several other existing models.