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.

A new family of distributions, called the Right truncated Xgamma-G, was developed. Explicit expressions for some of its statistical properties including the Renyi entropy, moments and generating functions, stress-strength reliability, Lorenz and Benferroni curves were established. The model parameters were estimated using the maximum likelihood estimation method and real-life application was provided using three datasets. It was also demonstrated that the Right truncated Xgamma-G family of distributions fits the datasets better than the Kumaraswamy-G, Beta-G, Exponentiated Generalized-G, Weibull-G, and Gompertz-G families of distributions.

In this paper, the symmetrical properties, numerical solution, and modelling of a big data set related to global warming are developed using of the Gaussian Mixed Distributions. The data is collected of daily temperatures from several cities over a 50-year period. In order to study the existence of the global warming precisely, the collected data is to be divided into two equal secondary periods, (i.e. from the years 1970 to 1994 and from 1995 to 2019). In addition, several methods of analysis will be applied in this research, especially with developing the EM algorithm having made the Maximum Likelihood method an important role in estimating the parameters of mixture models. Also, several models and tests like the Gaussian Mixed Distributions, the Kolmogorov-Smirnov and the Anderson-Darling tests, and the frequency distributions of the global warming data are developed in order to achieve good estimators, and optimal fitting. The techniques for assessing the model of mixture of the Gaussian Distribution Performance Model and the results of global warming data are discussed. In addition, the results of this paper have shown that the changes occurring in the climate in the studied cities are more severe than the changes occurring in the past (before 1970) and in other countries of Middle East region. In addition, the high average temperatures in the studied three governorates have indicated that Iraq's climate will be hotter and drier in the future.