This monograph is, as far as the author has gathered, the second of its kind (the first one was published by Nova in 2017 with coauthors Hamedani and Maadooliat) which presents various characterizations of a wide variety of continuous distributions. These two monographs could also be used as sources to prevent reinventing and duplicating the already exiting distributions. This current book consists of seven chapters. The first chapter lists cumulative and density functions of two hundred univariate distributions. Chapter two provides characterizations of these distributions: (i) based on the ration of two truncated moments; (ii) in terms of the hazard function; (iii) in terms of the reverse hazard function; (iv) based on the conditional expectation of certain functions of the random variable. Chapter three includes the characterizations of twenty distributions, including a published paper (Hamedani and Safavimanesh, 2017). Chapter four presents characterizations of thirty six distributions, and contains a published paper (Hamedani, 2017). Chapter five covers the characterizations of forty one distributions, as well as a published paper (Hamedani, 2018a). Chapter six presents characterizations of eighty distributions, and also contains a published paper (Hamedani, 2018b). Finally, chapter seven consists of seventy proposed distributions. The main reason to include previously published papers in Chapters 3-6 is to provide a rather complete source for the interested researchers who would want to avoid reinventing the existing distributions.

Provides in an organized manner characterizations of univariate probability distributions with many new results published in this area since the 1978 work of Golambos & Kotz "Characterizations of Probability Distributions" (Springer), together with applications of the theory in model fitting and predictions.

The definitive reference for statistical distributions Continuous Univariate Distributions, Volume 1 offers comprehensive guidance toward the most commonly used statistical distributions, including normal, lognormal, inverse Gaussian, Pareto, Cauchy, gamma distributions and more. Each distribution includes clear definitions and properties, plus methods of inference, applications, algorithms, characterizations, and reference to other related distributions. Organized for easy navigation and quick reference, this book is an invaluable resource for investors, data analysts, or anyone working with statistical distributions on a regular basis.

This Set Contains: Continuous Multivariate Distributions, Volume 1, Models and Applications, 2nd Edition by Samuel Kotz, N. Balakrishnan and Normal L. Johnson Continuous Univariate Distributions, Volume 1, 2nd Edition by Samuel Kotz, N. Balakrishnan and Normal L. Johnson Continuous Univariate Distributions, Volume 2, 2nd Edition by Samuel Kotz, N. Balakrishnan and Normal L. Johnson Discrete Multivariate Distributions by Samuel Kotz, N. Balakrishnan and Normal L. Johnson Univariate Discrete Distributions, 3rd Edition by Samuel Kotz, N. Balakrishnan and Normal L. Johnson Discover the latest advances in discrete distributions theory The Third Edition of the critically acclaimed Univariate Discrete Distributions provides a self-contained, systematic treatment of the theory, derivation, and application of probability distributions for count data. Generalized zeta-function and q-series distributions have been added and are covered in detail. New families of distributions, including Lagrangian-type distributions, are integrated into this thoroughly revised and updated text. Additional applications of univariate discrete distributions are explored to demonstrate the flexibility of this powerful method. A thorough survey of recent statistical literature draws attention to many new distributions and results for the classical distributions. Approximately 450 new references along with several new sections are introduced to reflect the current literature and knowledge of discrete distributions. Beginning with mathematical, probability, and statistical fundamentals, the authors provide clear coverage of the key topics in the field, including: Families of discrete distributions Binomial distribution Poisson distribution Negative binomial distribution Hypergeometric distributions Logarithmic and Lagrangian distributions Mixture distributions Stopped-sum distributions Matching, occupancy, runs, and q-series distributions Parametric regression models and miscellanea Emphasis continues to be placed on the increasing relevance of Bayesian inference to discrete distribution, especially with regard to the binomial and Poisson distributions. New derivations of discrete distributions via stochastic processes and random walks are introduced without unnecessarily complex discussions of stochastic processes. Throughout the Third Edition, extensive information has been added to reflect the new role of computer-based applications. With its thorough coverage and balanced presentation of theory and application, this is an excellent and essential reference for statisticians and mathematicians.

The book 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. Bayesian non-informative and conjugate priors are provided followed by a discussion on the distribution characteristics and applications in reliability engineering.

Comprehensive reference for statistical distributions Continuous Univariate Distributions, Volume 2 provides in-depth reference for anyone who applies statistical distributions in fields including engineering, business, economics, and the sciences. Covering a range of distributions, both common and uncommon, this book includes guidance toward extreme value, logistics, Laplace, beta, rectangular, noncentral distributions and more. Each distribution is presented individually for ease of reference, with clear explanations of methods of inference, tolerance limits, applications, characterizations, and other important aspects, including reference to other related distributions.