Welcome to Distribution Theory – II’s interesting world. I’m glad to give you this detailed book of Distribution Theory. For graduate students studying in the discipline of statistics, really there is no such complete book readily available. Students studying statistics at the degree, honours, and post-graduate levels will benefit from the current book. Students studying for numerous competitive exams would find the book useful as well. When writing this book, it was kept in mind that anyone reading it would find the topics easy to study and comprehend. Every eort has been taken to write the theorems or proofs in the simplest way feasible, and certain dicult parts have been splitted out with extensive explanations.
In order to create a resource that satisfies the needs of both students and professionals seeking a thorough understanding of the distribution theory, I drew on my experience as a teacher when writing this book. The structure of “Foundations of Distribution Theory – II” is designed to lead the reader logically and gradually through the subject matter. The framework for the next topic has been laid forth, as has an outline of the essential notions of distributions.
Reader may go at his/her own pace and gradually understand the nuances of distribution theory because there are thorough explanations, step-by-step derivations, and exercises with varied degrees of diculty included.
This book’s chapters cover six dierent probability distributions, each of which has unique properties and uses. In the first chapter, modelling the Weibull distribution, which is renowned for its adaptability in simulating a variety of events, from extreme value theory to reliability analysis is discussed in details. The Lognormal distribution is then discussed in the next chapter, where positive variables show patterns of multiplicative development, in areas such as economics, biology, and engineering. In the third chpater, truncated Normal distribution is the subject of the following discussion and offers a glimpse into the diffculties of working with constrained ranges as well as a demonstration of how truncation affects distribution features. The study of Laplace distribution continues in the fourth chapter. The fifth chapter discusses about the Pareto distribution which appears as a crucial player in understanding power dynamics, wealth distribution, and phenomena monitored by the “80-20 rule.” Its importance as a technique for capturing heavy-tailed distributions is highlighted by the fact that it appears across a variety of fields. The Bivariate Normal distribution, which depicts the relationship between two variables and gives insights into correlation and dependence, brings our voyage to a close.
I genuinely thank you, the reader, for your interest in and dedication to learning as you embark on this intellectual adventure. I’m hoping that this book will be a reliable companion that teaches you how to handle difficult problems and motivates additional research in this fascinating field..
I hope that your study on distribution theory is fruitful and enlightening.