Statistical distributions are important tools to model the characteristics of data sets such as right or left skewness, bi-modality or multi-modality observed in different applied sciences such as engineering, medicine, and finance, among others. The well-known distributions such as normal, Weibull, gamma, Lindley are extensively used because of their simple forms and identifiability properties. However, mostly in the last decade or so, researchers have focused on the more complex and flexible distributions, referred to as Generalized or simply G families of distributions to increase the modeling ability of these distributions by adding one or more shape parameters. The main aim of this edited book is to present new development currently made by various researchers in the field of G families of contributions distributions. The book will help future and current researchers in the field of this research. Some of the objectives are listed below: Develop new univariate continuous and discrete G families of probability distributions. Develop new bivariate continuous and discrete G families of probability distributions. Derive useful mathematical properties such as, ordinary and incomplete moments, moments generating functions, residual life and reversed residual life functions, order statistics, quantile spread ordering and entropies, among others and some bivariate and multivariate extensions of the new and existing models using a simple type copula such as: Farlie Gumbel Morgenstern copula. Modified Farlie Gumbel Morgenstern copula. Clayton copula. Renyi entropy copula. Ali-Mikhail-Haq copula. haracterize the models via several techniques such as: the conditional expectation. the truncated moment. the hazard functions. Mills ratio. certain functions of the random variable. the 1st order statistic. the conditional expectation of the record values. Assess the performance of the used estimation methods via Monte-Carlo simulation studies. Show the wide importance and the flexibility of the new models against the competitive models. Construct some new regression models based on the new proposed G families and use in statistical prediction. Application of many new useful goodness-of-fit tests for right censored validation such as the Nikulin-Rao-Robson goodness-of-fit test, modified Nikulin-Rao-Robson goodness-of-fit test, Bagdonavicius-Nikulin goodness-of-fit test and modified Bagdonavicius-Nikulin goodness-of-fit test to the new families.