Download or read book A Generalized Stochastic Process for Count Data written by Li Zhu and published by . This book was released on 2014 with total page 21 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Bernoulli and Poisson are two popular discrete count processes; however, both rely on strict assumptions that motivate their use. We instead propose a generalized count process (the Conway-Maxwell-Poisson process) that not only includes the Bernoulli and Poisson processes as special cases, but also serves as a flexible mechanism to describe count processes that approximate data with over- and under-dispersion. We introduce the process and its associated generalized waiting time distribution with several real-data applications to illustrate its flexibility for a variety of data structures.

Download or read book Stochastic Modeling of Scientific Data written by Peter Guttorp and published by CRC Press. This book was released on 2018-03-29 with total page 388 pages. Available in PDF, EPUB and Kindle. Book excerpt: Stochastic Modeling of Scientific Data combines stochastic modeling and statistical inference in a variety of standard and less common models, such as point processes, Markov random fields and hidden Markov models in a clear, thoughtful and succinct manner. The distinguishing feature of this work is that, in addition to probability theory, it contains statistical aspects of model fitting and a variety of data sets that are either analyzed in the text or used as exercises. Markov chain Monte Carlo methods are introduced for evaluating likelihoods in complicated models and the forward backward algorithm for analyzing hidden Markov models is presented. The strength of this text lies in the use of informal language that makes the topic more accessible to non-mathematicians. The combinations of hard science topics with stochastic processes and their statistical inference puts it in a new category of probability textbooks. The numerous examples and exercises are drawn from astronomy, geology, genetics, hydrology, neurophysiology and physics.

Download or read book Univariate Discrete Distributions written by Norman L. Johnson and published by John Wiley & Sons. This book was released on 2005-08-30 with total page 690 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book The Conway Maxwell Poisson Distribution written by Kimberly F. Sellers and published by Cambridge University Press. This book was released on 2023-02-28 with total page 356 pages. Available in PDF, EPUB and Kindle. Book excerpt: While the Poisson distribution is a classical statistical model for count data, the distributional model hinges on the constraining property that its mean equal its variance. This text instead introduces the Conway-Maxwell-Poisson distribution and motivates its use in developing flexible statistical methods based on its distributional form. This two-parameter model not only contains the Poisson distribution as a special case but, in its ability to account for data over- or under-dispersion, encompasses both the geometric and Bernoulli distributions. The resulting statistical methods serve in a multitude of ways, from an exploratory data analysis tool, to a flexible modeling impetus for varied statistical methods involving count data. The first comprehensive reference on the subject, this text contains numerous illustrative examples demonstrating R code and output. It is essential reading for academics in statistics and data science, as well as quantitative researchers and data analysts in economics, biostatistics and other applied disciplines.

Download or read book Analysis of Repeated Measures Data written by M. Ataharul Islam and published by Springer. This book was released on 2017-07-06 with total page 257 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a broad range of statistical techniques to address emerging needs in the field of repeated measures. It also provides a comprehensive overview of extensions of generalized linear models for the bivariate exponential family of distributions, which represent a new development in analysing repeated measures data. The demand for statistical models for correlated outcomes has grown rapidly recently, mainly due to presence of two types of underlying associations: associations between outcomes, and associations between explanatory variables and outcomes. The book systematically addresses key problems arising in the modelling of repeated measures data, bearing in mind those factors that play a major role in estimating the underlying relationships between covariates and outcome variables for correlated outcome data. In addition, it presents new approaches to addressing current challenges in the field of repeated measures and models based on conditional and joint probabilities. Markov models of first and higher orders are used for conditional models in addition to conditional probabilities as a function of covariates. Similarly, joint models are developed using both marginal-conditional probabilities as well as joint probabilities as a function of covariates. In addition to generalized linear models for bivariate outcomes, it highlights extended semi-parametric models for continuous failure time data and their applications in order to include models for a broader range of outcome variables that researchers encounter in various fields. The book further discusses the problem of analysing repeated measures data for failure time in the competing risk framework, which is now taking on an increasingly important role in the field of survival analysis, reliability and actuarial science. Details on how to perform the analyses are included in each chapter and supplemented with newly developed R packages and functions along with SAS codes and macro/IML. It is a valuable resource for researchers, graduate students and other users of statistical techniques for analysing repeated measures data.

Download or read book Modeling Count Data written by Joseph M. Hilbe and published by Cambridge University Press. This book was released on 2014-07-21 with total page 301 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides guidelines and fully worked examples of how to select, construct, interpret and evaluate the full range of count models.

Download or read book General Stochastic Processes in the Theory of Queues written by Václav E. Beneš and published by . This book was released on 1963 with total page 104 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Econometric Analysis of Count Data written by Rainer Winkelmann and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 291 pages. Available in PDF, EPUB and Kindle. Book excerpt: The primary objective of this book is to provide an introduction to the econometric modeling of count data for graduate students and researchers. It should serve anyone whose interest lies either in developing the field fur ther, or in applying existing methods to empirical questions. Much of the material included in this book is not specific to economics, or to quantita tive social sciences more generally, but rather extends to disciplines such as biometrics and technometrics. Applications are as diverse as the number of congressional budget vetoes, the number of children in a household, and the number of mechanical defects in a production line. The unifying theme is a focus on regression models in which a dependent count variable is modeled as a function of independent variables which mayor may not be counts as well. The modeling of count data has come of age. Inclusion of some of the fundamental models in basic textbooks, and implementation on standard computer software programs bear witness to that. Based on the standard Poisson regression model, numerous extensions and alternatives have been developed to address the common challenges faced in empirical modeling (unobserved heterogeneity, selectivity, endogeneity, measurement error, and dependent observations in the context of panel data or multivariate data, to name but a few) as well as the challenges that are specific to count data (e. g. , over dispersion and underdispersion).

Download or read book Statistical Analysis of Panel Count Data written by Jianguo Sun and published by Springer Science & Business Media. This book was released on 2013-10-09 with total page 283 pages. Available in PDF, EPUB and Kindle. Book excerpt: Panel count data occur in studies that concern recurrent events, or event history studies, when study subjects are observed only at discrete time points. By recurrent events, we mean the event that can occur or happen multiple times or repeatedly. Examples of recurrent events include disease infections, hospitalizations in medical studies, warranty claims of automobiles or system break-downs in reliability studies. In fact, many other fields yield event history data too such as demographic studies, economic studies and social sciences. For the cases where the study subjects are observed continuously, the resulting data are usually referred to as recurrent event data. This book collects and unifies statistical models and methods that have been developed for analyzing panel count data. It provides the first comprehensive coverage of the topic. The main focus is on methodology, but for the benefit of the reader, the applications of the methods to real data are also discussed along with numerical calculations. There exists a great deal of literature on the analysis of recurrent event data. This book fills the void in the literature on the analysis of panel count data. This book provides an up-to-date reference for scientists who are conducting research on the analysis of panel count data. It will also be instructional for those who need to analyze panel count data to answer substantive research questions. In addition, it can be used as a text for a graduate course in statistics or biostatistics that assumes a basic knowledge of probability and statistics.

Download or read book Essentials of Stochastic Processes written by Richard Durrett and published by Springer. This book was released on 2016-11-07 with total page 282 pages. Available in PDF, EPUB and Kindle. Book excerpt: Building upon the previous editions, this textbook is a first course in stochastic processes taken by undergraduate and graduate students (MS and PhD students from math, statistics, economics, computer science, engineering, and finance departments) who have had a course in probability theory. It covers Markov chains in discrete and continuous time, Poisson processes, renewal processes, martingales, and option pricing. One can only learn a subject by seeing it in action, so there are a large number of examples and more than 300 carefully chosen exercises to deepen the reader’s understanding. Drawing from teaching experience and student feedback, there are many new examples and problems with solutions that use TI-83 to eliminate the tedious details of solving linear equations by hand, and the collection of exercises is much improved, with many more biological examples. Originally included in previous editions, material too advanced for this first course in stochastic processes has been eliminated while treatment of other topics useful for applications has been expanded. In addition, the ordering of topics has been improved; for example, the difficult subject of martingales is delayed until its usefulness can be applied in the treatment of mathematical finance.

Download or read book Statistical Models Based on Counting Processes written by Per K. Andersen and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 779 pages. Available in PDF, EPUB and Kindle. Book excerpt: Modern survival analysis and more general event history analysis may be effectively handled within the mathematical framework of counting processes. This book presents this theory, which has been the subject of intense research activity over the past 15 years. The exposition of the theory is integrated with careful presentation of many practical examples, drawn almost exclusively from the authors'own experience, with detailed numerical and graphical illustrations. Although Statistical Models Based on Counting Processes may be viewed as a research monograph for mathematical statisticians and biostatisticians, almost all the methods are given in concrete detail for use in practice by other mathematically oriented researchers studying event histories (demographers, econometricians, epidemiologists, actuarial mathematicians, reliability engineers and biologists). Much of the material has so far only been available in the journal literature (if at all), and so a wide variety of researchers will find this an invaluable survey of the subject.

Download or read book An Introduction to Stochastic Modeling written by Howard M. Taylor and published by Academic Press. This book was released on 2014-05-10 with total page 410 pages. Available in PDF, EPUB and Kindle. Book excerpt: An Introduction to Stochastic Modeling provides information pertinent to the standard concepts and methods of stochastic modeling. This book presents the rich diversity of applications of stochastic processes in the sciences. Organized into nine chapters, this book begins with an overview of diverse types of stochastic models, which predicts a set of possible outcomes weighed by their likelihoods or probabilities. This text then provides exercises in the applications of simple stochastic analysis to appropriate problems. Other chapters consider the study of general functions of independent, identically distributed, nonnegative random variables representing the successive intervals between renewals. This book discusses as well the numerous examples of Markov branching processes that arise naturally in various scientific disciplines. The final chapter deals with queueing models, which aid the design process by predicting system performance. This book is a valuable resource for students of engineering and management science. Engineers will also find this book useful.

Download or read book Regression Analysis of Count Data written by A. Colin Cameron and published by Cambridge University Press. This book was released on 2013-05-27 with total page 597 pages. Available in PDF, EPUB and Kindle. Book excerpt: Students in both social and natural sciences often seek regression methods to explain the frequency of events, such as visits to a doctor, auto accidents, or new patents awarded. This book, now in its second edition, provides the most comprehensive and up-to-date account of models and methods to interpret such data. The authors combine theory and practice to make sophisticated methods of analysis accessible to researchers and practitioners working with widely different types of data and software in areas such as applied statistics, econometrics, marketing, operations research, actuarial studies, demography, biostatistics and quantitative social sciences. The new material includes new theoretical topics, an updated and expanded treatment of cross-section models, coverage of bootstrap-based and simulation-based inference, expanded treatment of time series, multivariate and panel data, expanded treatment of endogenous regressors, coverage of quantile count regression, and a new chapter on Bayesian methods.

Download or read book Stochastic Models Statistics and Their Applications written by Ansgar Steland and published by Springer. This book was released on 2015-02-04 with total page 479 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume presents the latest advances and trends in stochastic models and related statistical procedures. Selected peer-reviewed contributions focus on statistical inference, quality control, change-point analysis and detection, empirical processes, time series analysis, survival analysis and reliability, statistics for stochastic processes, big data in technology and the sciences, statistical genetics, experiment design, and stochastic models in engineering. Stochastic models and related statistical procedures play an important part in furthering our understanding of the challenging problems currently arising in areas of application such as the natural sciences, information technology, engineering, image analysis, genetics, energy and finance, to name but a few. This collection arises from the 12th Workshop on Stochastic Models, Statistics and Their Applications, Wroclaw, Poland.

Download or read book Regression Analysis of Count Data written by Adrian Colin Cameron and published by Cambridge University Press. This book was released on 2013-05-27 with total page 597 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides the most comprehensive and up-to-date account of regression methods to explain the frequency of events.

Download or read book Count Data Models written by Rainer Winkelmann and published by Springer Science & Business Media. This book was released on 2013-11-11 with total page 223 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents statistical methods for the analysis of events. The primary focus is on single equation cross section models. The book addresses both the methodology and the practice of the subject and it provides both a synthesis of a diverse body of literature that hitherto was available largely in pieces, as well as a contribution to the progress of the methodology, establishing several new results and introducing new models. Starting from the standard Poisson regression model as a benchmark, the causes, symptoms and consequences of misspecification are worked out. Both parametric and semi-parametric alternatives are discussed. While semi-parametric models allow for robust interference, parametric models can identify features of the underlying data generation process.

Download or read book The Analysis of Stochastic Processes using GLIM written by James K. Lindsey and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 301 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of this book is to present a survey of the many ways in which the statistical package GLIM may be used to model and analyze stochastic processes. Its emphasis is on using GLIM interactively to apply statistical techniques, and examples are drawn from a wide range of applications including medicine, biology, and the social sciences. It is based on the author's many years of teaching courses along these lines to both undergraduate and graduate students. The author assumes that readers have a reasonably strong background in statistics such as might be gained from undergraduate courses and that they are also familiar with the basic workings of GLIM. Topics covered include: the analysis of survival data, regression and fitting distributions, time series analysis (including both the time and frequency domains), repeated measurements, and generalized linear models.