The q_T-X family of distributions induced by V is inspired by [Clement Boateng Ampadu, Quantile-Generated Family of Distributions: A New Method for Generating Continuous Distributions, Fundamental Journal of Mathematics and Mathematical Sciences, Volume 9, Issue 1, 2018, Pages 13-34]. This book investigates some properties and applications of a somewhat dual to the EG T-X family of distributions that appeared in [Suleman Nasiru, Peter N. Mwita and Oscar Ngesa, Exponentiated Generalized Transformed-Transformer Family of Distributions, Journal of Statistical and Econometric Methods, vol.6, no.4, 2017, 1-17]. A notable feature of the book are the exercise sets, and the section "Further Developments", which invites the reader to begin his or her own investigative inquiry into quantile generated probability distributions.