Large Sample Theory

Large Sample Theory provides an accessible and rigorous introduction to the asymptotic theory related to large samples. It contains most of the topics related to large samples. It includes order statistics, central limit theorem, extreme Values and record statistics. The materials of the book are developed from the very elementary level to the research level. The mathematical backgrounds needed for the materials of the book are basic knowledge of calculus and probability, The topics that are included in chapter 1 are Limit theory, convergence in probability, convergence in distribution and some basic theory of probability including characteristic functions and their applications. Chapter 1 also contains list of common probability distributions and some of their basic properties, few basic description of exchangeable random variables, m-dependent sequence and martingales that are needed in the development of other chapters. This book is intended for students and applied scientists dealing with statistics and data science.