Extended Families of Probability Distributions and Their Applications

This book arose from our experience as active researchers working in the field of probability distributions and have derived classes, families and systems of probability distributions in our research during the past two decades. We had noticed that it was appropriate to put forward a set of choices and ideas that were used after the forties of the past century and before the emergence of influential probability distributions, which paved the way for their current enormous development. In particular, we indicate to the the family of gamma distributions, the expansive extensions of the parameters, and the general forms that generalize its basic form, in addition to the extension of the mixture of gamma that leads to Lindley model and its various generalizations. The astonishing computational ability of personal computing is now making cutting edge inferential technologies seamlessly accessible. Although the computing power available is more than equal to the task, many powerful techniques for extracting the most information from expensive data are not as widely adopted as they should be due to the unavailability of appropriate software. We tried to write this book that we wanted to be out five years ago, and we began to organize the material for research and review the most important research ideas on the topic at the level of statistics, quality control, reliability engineering, fitting and simulation, among others. We have considered the necessary license for using published material in order to include a lot of material in the current form of the book