Probability Distribution

This book, developed by the University of Maryland Center for Risk and Reliability, published by the RIAC, and used as a supplemental reference book in courses offered by the University of Maryland, provides details on 22 probability distributions. Each distribution section provides a graphical visualization and formulas for distribution parameters, along with distribution formulas. Common statistics such as moments and percentile formulas are followed by likelihood functions and in many cases the derivation of maximum likelihood estimates.

Lagrangian expansions can be used to obtain numerous useful probability models, which have been applied to real life situations including, but not limited to: branching processes, queuing processes, stochastic processes, environmental toxicology, diffusion of information, ecology, strikes in industries, sales of new products, and production targets for optimum profits. This book presents a comprehensive, systematic treatment of the class of Lagrangian probability distributions, along with some of its families, their properties, and important applications.

Inequality has become an essential tool in many areas of mathematical research, for example in probability and statistics where it is frequently used in the proofs. "Probability Inequalities" covers inequalities related with events, distribution functions, characteristic functions, moments and random variables (elements) and their sum. The book shall serve as a useful tool and reference for scientists in the areas of probability and statistics, and applied mathematics.