In this paper, we propose a flexible and general family of distributions based on an original power-exponential transformation approach. We call it the modified generalized-G (MGG) family. The elegance and significance of this family lie in the ability to modify the standard distributions by changing their functional forms without adding new parameters, by compounding two distributions, or by adding one or two shape parameters. The aim of this modification is to provide flexible shapes for the corresponding probability functions. In particular, the distributions of the MGG family can possess increasing, constant, decreasing, “unimodal”, or “bathtub-shaped“ hazard rate functions, which are ideal for fitting several real data sets encountered in applied fields. Some members of the MGG family are proposed for special distributions. Following that, the uniform distribution is chosen as a baseline distribution to yield the modified uniform (MU) distribution with the goal of efficiently modeling measures with bounded values. Some useful key properties of the MU distribution are determined. The estimation of the unknown parameters of the MU model is discussed using seven methods, and then, a simulation study is carried out to explore the performance of the estimates. The flexibility of this model is illustrated by the analysis of two real-life data sets. When compared to fair and well-known competitor models in contemporary literature, better-fitting results are obtained for the new model.

Employing the inverse power transformation technique, we have proposed a new continuous three-parameter probability distribution and named it inverse power generalized Maxwell distribution. This distribution is the generalized version of the generalized Maxwell distribution. For this model, we have derived some functions related to survival analysis. Several statistical properties of the model are provided. This study also focused on the estimation of the unknown model parameters. Six different parameter estimation methods are employed and studied extensively through numerical simulation. To investigate the applications of the suggested model, two real engineering data sets are considered and empirically found that the suggested model can provide a superior fit as compared to some candidate models under study.\\ \\ \textbf{Keywords:} Generalize Maxwell distribution, Moments, Estimation, Inverse power, Entropy.