Lagrangian Probability Distributions

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. Graduate students and researchers with a good knowledge of standard statistical techniques and an interest in Lagrangian probability distributions will find this work valuable. It may be used as a reference text or in courses and seminars on Distribution Theory and Lagrangian Distributions. Applied scientists and researchers in environmental statistics, reliability, sales management, epidemiology, operations research, optimization in manufacturing and marketing, and infectious disease control will benefit immensely from the various applications in the book.

Table of Contents:
Preliminary Information.- Lagrangian Probability Distributions.- Properties of General Lagrangian Distributions.- Quasi-Probability Models.- Some Urn Models.- Development of Models and Applications.- Modified Power Series Distributions.- Some Basic Lagrangian Distributions.- Generalized Poisson Distribution.- Generalized Negative Binomial Distribution.- Generalized Logarithmic Series Distribution.- Lagrangian Katz Distribution.- Random Walks and Jump Models.- Bivariate Lagrangian Distributions.- Multivariate Lagrangian Distributions.- Computer Generation of Lagrangian Variables.

Review :
From the reviews: "The book is the first comprehensive presentation of the theory of distributions which are derived and/or closely connected with Lagrange expansions. It gives an overview of the research on this topic published during the last thirty-five years. The text is illustrated with many surprising examples. The book can be recommended for both applied and theoretical statistics." —Mathematical Reviews "The purpose of this book is to collect most of the research materials in the various journals during the last thirtyfive years and to give a reasonable and systematic account of the class of Lagrangian distributions and some of their properties and applications. … it is meant for graduate students and researchers who have knowledge of standard statistical techniques. Every chapter … are supplied with exercises. The list of references contains 252 positions. The volume of the book is over 350 pages." (Nijole Kalinauskaite, Zentralblatt MATH, Vol. 1101 (3), 2007) “The book acquaints researchers and graduate students with good mathematical, probabilistic and statistical knowledge, with the present-day stage of the theory of distributions derived from and/or closely connected with Lagrange expansions. … The authors are leading persons in the field. They collected most of the results published in various journals during the last forty years and their work can be considered a textbook for advanced courses and seminars in theoretical and/or applied statistics.” (Gejza Wimmer, Applications of Mathematics, Vol. 56 (6), 2011)