Representative Points of Statistical Distributions

Statistical simulation has become a cornerstone in statistical research and applications. The aim of the book is to present a comprehensive exploration of various methods for statistical simulation and resampling, focusing on consistency and efficiency. It covers a range of representative points (RPs) Monte Carlo (MC) RPs, Quasi-Monte Carlo (QMC) RPs, and Mean Square Error (MSE) RPs and their applications, and includes a collection of recent developments in the field. It also explores other types of representative points, and the corresponding approximate distributions, and delves into the realm of statistical simulation, by exploring the limitations of traditional Monte Carlo methods and the innovations brought about by the bootstrap method. It also introduces other kinds of representative points and the corresponding approximate distributions, such as quasi-Monte Carlo and mean square error methods. Features: Comprehensive exploration of statistical simulation methods: It provides a deep dive into MC methods, Bootstrap methods, and introduces other kinds of representative points and the corresponding approximate distributions, such as quasi-Monte Carlo and mean square error methods. Emphasis on consistency and efficiency: It highlights the advantages of these methods in terms of consistency and efficiency, addressing the slow convergence rate of classical statistical simulation. Collection of recent developments: It brings together the latest advancements in the field of statistical simulation, keeping readers up-to-date with the most current research. Practical applications: The book includes numerous practical applications of various types of representative points (MC-RPs, QMC-RPs, and MSE-RPs) in statistical inference and simulation. Educational resource: It can serve as a textbook for postgraduate students, a reference book for undergraduate students, and a valuable resource for professionals in various fields. The book serves as a valuable resource for postgraduate students, researchers, and practitioners in statistics, mathematics, and other quantitative fields.