ABSTRACT
This introduction presents an overview of the key concepts discussed in the subsequent chapters of this book. The book presents a short review of the key results on distribution functions from Books I and II. It analyses transformations of random variables. The book introduces expectations of random variables and transformed random variables in the general context of a Riemann-Stieltjes integral. It then exemplifies simulation approaches for discrete distributions, and then continuous distributions, using the left-continuous inverse function F∗(y) and independent, continuous uniform variates commonly provided by various mathematical software. The book also presents a formal short review of the theoretical framework of Book II for the construction of a probability space on which a countable collection of independent, identically distributed random variables can be defined, and thus on which limit theorems of various types can be addressed. It focuses on two main themes. The first topic is large deviation theory and the second major section is on extreme value theory.
