Stochastic equations through the eye of the physicist

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N. Balakrishnan

"Presenting a concise, well-rounded focus on the statistical concepts and applications that are essential for understanding gathered data in the earth and atmospheric sciences. Containing contributions from over 100 leading academics, researchers, and practitioners in these fields, this comprehensive book unveils modern, approaches to the acquisition and analysis of data across diverse subject areas like geology, agriculture, animal science, and geophysics. It discusses techniques related to survey methodology, computational statistics, and operations research and covers new areas of interest like non-linear weather forecasting, construction geological surveys, and water pollution assessment"-- "Provides a realistic alternative to the individual user who would like a quick reference containing encyclopedic information that pertains to their particular research interests and needs"--

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Joseph M. Hilbe

"This second edition of Hilbe's Negative Binomial Regression is a substantial enhancement to the popular first edition. The only text devoted entirely to the negative binomial model and its many variations, nearly every model discussed in the literature is addressed. The theoretical and distributional background of each model is discussed, together with examples of their construction, application, interpretation, and evaluation. Complete Stata and R code are provided throughout the text, with additional code (plus SAS), derivations, and data provided on the book's website. Written for the practicing researcher, the text begins with an examination of risk and rate ratios, and of the estimating algorithms used to model count data. The book then gives an in-depth analysis of Poisson regression and an evaluation of the meaning and nature of overdispersion, followed by a comprehensive analysis of the negative binomial distribution and of its parameterizations into various models for evaluating count data"--

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C. Radhakrishna Rao, D.N. Shanbhag

The ICFE was originally introduced to characterize a probability distribution by some invariant property under a stochastic change (damage) to the original random variable, and it is a generalization of a certain version of the Choquet-Deny convolution equation which occurs in potential theory. The solution of the ICFE is obtained using certain properties of exchangeable random elements or martingales, amongst other things. The solutions to these functional equations provide a unified and elegant approach to characterizations of the exponential, geometric, Pareto, Weibull, stable, Poisson and other distributions under a variety of stochastic properties of the random variable. The ICFE also plays an important role in renewal processes, potential theory and other applications of stochastic processes. Several illustrative examples are given to show the wide applicability of the ICFE. Besides the general theory associated with the ICFE and related equations, the book introduces new probability tools and techniques which should be of interest to research workers in probability and statistics, as well as those working in other areas such as biology, medicine and engineering.

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Stefan Turek

This book discusses recent numerical and algorithmic tools for the solution of certain flow problems arising in Computational Fluid Dynamics (CFD), which are governed by the incompressible Navier-Stokes equations. It contains several of the latest results for the numerical solution of (complex) flow problems on modern computer platforms. Particular emphasis is put on the solution process of the resulting high dimensional discrete systems of equations which is often neglected in other works. Together with the included CD ROM which contains the complete FEATFLOW 1.1 software and parts of the "Virtual Album of Fluid Motion", which is a "Movie Gallery" with lots of MPED videos, the interested reader is enabled to perform his own numerical simulations or he may find numerous suggestions for improving his own computational simulations.