The Conway Maxwell Poisson Distribution

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The Conway Maxwell Poisson Distribution

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Author : Kimberly F. Sellers
language : en
Publisher: Cambridge University Press
Release Date : 2023-03-09

The Conway Maxwell Poisson Distribution written by Kimberly F. Sellers and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-03-09 with Mathematics categories.

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.

An Introduction To Stein S Method

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Author : Andrew Barbour
language : en
Publisher: World Scientific
Release Date : 2005-04-14

An Introduction To Stein S Method written by Andrew Barbour and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-04-14 with Mathematics categories.

A common theme in probability theory is the approximation of complicated probability distributions by simpler ones, the central limit theorem being a classical example. Stein's method is a tool which makes this possible in a wide variety of situations. Traditional approaches, for example using Fourier analysis, become awkward to carry through in situations in which dependence plays an important part, whereas Stein's method can often still be applied to great effect. In addition, the method delivers estimates for the error in the approximation, and not just a proof of convergence. Nor is there in principle any restriction on the distribution to be approximated; it can equally well be normal, or Poisson, or that of the whole path of a random process, though the techniques have so far been worked out in much more detail for the classical approximation theorems.This volume of lecture notes provides a detailed introduction to the theory and application of Stein's method, in a form suitable for graduate students who want to acquaint themselves with the method. It includes chapters treating normal, Poisson and compound Poisson approximation, approximation by Poisson processes, and approximation by an arbitrary distribution, written by experts in the different fields. The lectures take the reader from the very basics of Stein's method to the limits of current knowledge.

Poisson Approximation

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Author : A. D. Barbour
language : en
Publisher:
Release Date : 2023

Poisson Approximation written by A. D. Barbour and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023 with Approximation theory categories.

The Poisson 'law of small numbers' is a central principle in modern theories of reliability, insurance and the statistics of extremes. It also has ramifications in apparently unrelated areas, such as the description of algebraic and combinatorial structures and the distribution of prime numbers. This book provides an introduction to the method and a varied selection of examples of its application, emphasizing the flexibility of the technique when combined with a judicious choice of coupling.

Introduction To Statistical Process Control

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Author : Muhammad Aslam
language : en
Publisher: John Wiley & Sons
Release Date : 2020-09-16

Introduction To Statistical Process Control written by Muhammad Aslam and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-09-16 with Mathematics categories.

An Introduction to the Fundamentals and History of Control Charts, Applications, and Guidelines for Implementation Introduction to Statistical Process Control examines various types of control charts that are typically used by engineering students and practitioners. This book helps readers develop a better understanding of the history, implementation, and use-cases. Students are presented with varying control chart techniques, information, and roadmaps to ensure their control charts are operating efficiently and producing specification-confirming products. This is the essential text on the theories and applications behind statistical methods and control procedures. This eight-chapter reference breaks information down into digestible sections and covers topics including: ● An introduction to the basics as well as a background of control charts ● Widely used and newly researched attributes of control charts, including guidelines for implementation ● The process capability index for both normal and non-normal distribution via the sampling of multiple dependent states ● An overview of attribute control charts based on memory statistics ● The development of control charts using EQMA statistics For a solid understanding of control methodologies and the basics of quality assurance, Introduction to Statistical Process Control is a definitive reference designed to be read by practitioners and students alike. It is an essential textbook for those who want to explore quality control and systems design.

Modeling Count Data

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Author : Joseph M. Hilbe
language : en
Publisher: Cambridge University Press
Release Date : 2014-07-21

Modeling Count Data written by Joseph M. Hilbe and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-07-21 with Business & Economics categories.

This book provides guidelines and fully worked examples of how to select, construct, interpret and evaluate the full range of count models.

An Introduction To Discrete Valued Time Series

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Author : Christian H. Weiss
language : en
Publisher: John Wiley & Sons
Release Date : 2018-02-05

An Introduction To Discrete Valued Time Series written by Christian H. Weiss and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-02-05 with Mathematics categories.

A much-needed introduction to the field of discrete-valued time series, with a focus on count-data time series Time series analysis is an essential tool in a wide array of fields, including business, economics, computer science, epidemiology, finance, manufacturing and meteorology, to name just a few. Despite growing interest in discrete-valued time series—especially those arising from counting specific objects or events at specified times—most books on time series give short shrift to that increasingly important subject area. This book seeks to rectify that state of affairs by providing a much needed introduction to discrete-valued time series, with particular focus on count-data time series. The main focus of this book is on modeling. Throughout numerous examples are provided illustrating models currently used in discrete-valued time series applications. Statistical process control, including various control charts (such as cumulative sum control charts), and performance evaluation are treated at length. Classic approaches like ARMA models and the Box-Jenkins program are also featured with the basics of these approaches summarized in an Appendix. In addition, data examples, with all relevant R code, are available on a companion website. Provides a balanced presentation of theory and practice, exploring both categorical and integer-valued series Covers common models for time series of counts as well as for categorical time series, and works out their most important stochastic properties Addresses statistical approaches for analyzing discrete-valued time series and illustrates their implementation with numerous data examples Covers classical approaches such as ARMA models, Box-Jenkins program and how to generate functions Includes dataset examples with all necessary R code provided on a companion website An Introduction to Discrete-Valued Time Series is a valuable working resource for researchers and practitioners in a broad range of fields, including statistics, data science, machine learning, and engineering. It will also be of interest to postgraduate students in statistics, mathematics and economics.

Generalized Linear Models

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Author : Raymond H. Myers
language : en
Publisher: John Wiley & Sons
Release Date : 2012-01-20

Generalized Linear Models written by Raymond H. Myers and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-01-20 with Mathematics categories.

Praise for the First Edition "The obvious enthusiasm of Myers, Montgomery, and Vining and their reliance on their many examples as a major focus of their pedagogy make Generalized Linear Models a joy to read. Every statistician working in any area of applied science should buy it and experience the excitement of these new approaches to familiar activities." —Technometrics Generalized Linear Models: With Applications in Engineering and the Sciences, Second Edition continues to provide a clear introduction to the theoretical foundations and key applications of generalized linear models (GLMs). Maintaining the same nontechnical approach as its predecessor, this update has been thoroughly extended to include the latest developments, relevant computational approaches, and modern examples from the fields of engineering and physical sciences. This new edition maintains its accessible approach to the topic by reviewing the various types of problems that support the use of GLMs and providing an overview of the basic, related concepts such as multiple linear regression, nonlinear regression, least squares, and the maximum likelihood estimation procedure. Incorporating the latest developments, new features of this Second Edition include: A new chapter on random effects and designs for GLMs A thoroughly revised chapter on logistic and Poisson regression, now with additional results on goodness of fit testing, nominal and ordinal responses, and overdispersion A new emphasis on GLM design, with added sections on designs for regression models and optimal designs for nonlinear regression models Expanded discussion of weighted least squares, including examples that illustrate how to estimate the weights Illustrations of R code to perform GLM analysis The authors demonstrate the diverse applications of GLMs through numerous examples, from classical applications in the fields of biology and biopharmaceuticals to more modern examples related to engineering and quality assurance. The Second Edition has been designed to demonstrate the growing computational nature of GLMs, as SAS®, Minitab®, JMP®, and R software packages are used throughout the book to demonstrate fitting and analysis of generalized linear models, perform inference, and conduct diagnostic checking. Numerous figures and screen shots illustrating computer output are provided, and a related FTP site houses supplementary material, including computer commands and additional data sets. Generalized Linear Models, Second Edition is an excellent book for courses on regression analysis and regression modeling at the upper-undergraduate and graduate level. It also serves as a valuable reference for engineers, scientists, and statisticians who must understand and apply GLMs in their work.

Asymptotic Expansions Of Integrals

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Author : Norman Bleistein
language : en
Publisher: Courier Corporation
Release Date : 1986-01-01

Asymptotic Expansions Of Integrals written by Norman Bleistein and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 1986-01-01 with Mathematics categories.

Excellent introductory text, written by two experts, presents a coherent and systematic view of principles and methods. Topics include integration by parts, Watson's lemma, LaPlace's method, stationary phase, and steepest descents. Additional subjects include the Mellin transform method and less elementary aspects of the method of steepest descents. 1975 edition.

Perturbation Methods

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Author : E. J. Hinch
language : en
Publisher: Cambridge University Press
Release Date : 1991-10-25

Perturbation Methods written by E. J. Hinch and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1991-10-25 with Mathematics categories.

A textbook presenting the theory and underlying techniques of perturbation methods in a manner suitable for senior undergraduates from a broad range of disciplines.

Statistics For Process Control Engineers

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Author : Myke King
language : en
Publisher: John Wiley & Sons
Release Date : 2017-10-23

Statistics For Process Control Engineers written by Myke King and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-10-23 with Technology & Engineering categories.

The first statistics guide focussing on practical application to process control design and maintenance Statistics for Process Control Engineers is the only guide to statistics written by and for process control professionals. It takes a wholly practical approach to the subject. Statistics are applied throughout the life of a process control scheme – from assessing its economic benefit, designing inferential properties, identifying dynamic models, monitoring performance and diagnosing faults. This book addresses all of these areas and more. The book begins with an overview of various statistical applications in the field of process control, followed by discussions of data characteristics, probability functions, data presentation, sample size, significance testing and commonly used mathematical functions. It then shows how to select and fit a distribution to data, before moving on to the application of regression analysis and data reconciliation. The book is extensively illustrated throughout with line drawings, tables and equations, and features numerous worked examples. In addition, two appendices include the data used in the examples and an exhaustive catalogue of statistical distributions. The data and a simple-to-use software tool are available for download. The reader can thus reproduce all of the examples and then extend the same statistical techniques to real problems. Takes a back-to-basics approach with a focus on techniques that have immediate, practical, problem-solving applications for practicing engineers, as well as engineering students Shows how to avoid the many common errors made by the industry in applying statistics to process control Describes not only the well-known statistical distributions but also demonstrates the advantages of applying the large number that are less well-known Inspires engineers to identify new applications of statistical techniques to the design and support of control schemes Provides a deeper understanding of services and products which control engineers are often tasked with assessing This book is a valuable professional resource for engineers working in the global process industry and engineering companies, as well as students of engineering. It will be of great interest to those in the oil and gas, chemical, pulp and paper, water purification, pharmaceuticals and power generation industries, as well as for design engineers, instrument engineers and process technical support.