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Distributions

Author : J.J. Duistermaat

Publisher : Springer Science & Business Media

Page : 455 pages

File Size : 18,9 MB

Release : 2010-08-09

Category : Mathematics

ISBN : 0817646752

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Book Description

This textbook is an application-oriented introduction to the theory of distributions, a powerful tool used in mathematical analysis. The treatment emphasizes applications that relate distributions to linear partial differential equations and Fourier analysis problems found in mechanics, optics, quantum mechanics, quantum field theory, and signal analysis. The book is motivated by many exercises, hints, and solutions that guide the reader along a path requiring only a minimal mathematical background.



Statistical Distributions

Author : Catherine Forbes

Publisher : John Wiley & Sons

Page : 206 pages

File Size : 10,80 MB

Release : 2011-03-21

Category : Mathematics

ISBN : 1118097823

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Book Description

A new edition of the trusted guide on commonly used statistical distributions Fully updated to reflect the latest developments on the topic, Statistical Distributions, Fourth Edition continues to serve as an authoritative guide on the application of statistical methods to research across various disciplines. The book provides a concise presentation of popular statistical distributions along with the necessary knowledge for their successful use in data modeling and analysis. Following a basic introduction, forty popular distributions are outlined in individual chapters that are complete with related facts and formulas. Reflecting the latest changes and trends in statistical distribution theory, the Fourth Edition features: A new chapter on queuing formulas that discusses standard formulas that often arise from simple queuing systems Methods for extending independent modeling schemes to the dependent case, covering techniques for generating complex distributions from simple distributions New coverage of conditional probability, including conditional expectations and joint and marginal distributions Commonly used tables associated with the normal (Gaussian), student-t, F and chi-square distributions Additional reviewing methods for the estimation of unknown parameters, such as the method of percentiles, the method of moments, maximum likelihood inference, and Bayesian inference Statistical Distributions, Fourth Edition is an excellent supplement for upper-undergraduate and graduate level courses on the topic. It is also a valuable reference for researchers and practitioners in the fields of engineering, economics, operations research, and the social sciences who conduct statistical analyses.



Finite Mixture Distributions

Author : B. Everitt

Publisher : Springer Science & Business Media

Page : 148 pages

File Size : 35,26 MB

Release : 2013-03-08

Category : Science

ISBN : 9400958978

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Book Description

Finite mixture distributions arise in a variety of applications ranging from the length distribution of fish to the content of DNA in the nuclei of liver cells. The literature surrounding them is large and goes back to the end of the last century when Karl Pearson published his well-known paper on estimating the five parameters in a mixture of two normal distributions. In this text we attempt to review this literature and in addition indicate the practical details of fitting such distributions to sample data. Our hope is that the monograph will be useful to statisticians interested in mixture distributions and to re search workers in other areas applying such distributions to their data. We would like to express our gratitude to Mrs Bertha Lakey for typing the manuscript. Institute oj Psychiatry B. S. Everitt University of London D. l Hand 1980 CHAPTER I General introduction 1. 1 Introduction This monograph is concerned with statistical distributions which can be expressed as superpositions of (usually simpler) component distributions. Such superpositions are termed mixture distributions or compound distributions. For example, the distribution of height in a population of children might be expressed as follows: h(height) = fg(height: age)f(age)d age (1. 1) where g(height: age) is the conditional distribution of height on age, and/(age) is the age distribution of the children in the population.



Comparing Distributions

Author : Olivier Thas

Publisher : Springer Science & Business Media

Page : 358 pages

File Size : 36,92 MB

Release : 2010-03-14

Category : Mathematics

ISBN : 0387927107

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Book Description

Provides a self-contained comprehensive treatment of both one-sample and K-sample goodness-of-fit methods by linking them to a common theory backbone Contains many data examples, including R-code and a specific R-package for comparing distributions Emphesises informative statistical analysis rather than plain statistical hypothesis testing



A Primer on Statistical Distributions

Author : Narayanaswamy Balakrishnan

Publisher : John Wiley & Sons

Page : 322 pages

File Size : 50,70 MB

Release : 2004-12-04

Category : Mathematics

ISBN : 0471722219

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Book Description

Designed as an introduction to statistical distribution theory. * Includes a first chapter on basic notations and definitions that are essential to working with distributions. * Remaining chapters are divided into three parts: Discrete Distributions, Continuous Distributions, and Multivariate Distributions. * Exercises are incorporated throughout the text in order to enhance understanding of materials just taught.



Univariate Stable Distributions

Author : John P. Nolan

Publisher : Springer Nature

Page : 342 pages

File Size : 31,17 MB

Release : 2020-09-13

Category : Mathematics

ISBN : 3030529150

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Book Description

This textbook highlights the many practical uses of stable distributions, exploring the theory, numerical algorithms, and statistical methods used to work with stable laws. Because of the author’s accessible and comprehensive approach, readers will be able to understand and use these methods. Both mathematicians and non-mathematicians will find this a valuable resource for more accurately modelling and predicting large values in a number of real-world scenarios. Beginning with an introductory chapter that explains key ideas about stable laws, readers will be prepared for the more advanced topics that appear later. The following chapters present the theory of stable distributions, a wide range of applications, and statistical methods, with the final chapters focusing on regression, signal processing, and related distributions. Each chapter ends with a number of carefully chosen exercises. Links to free software are included as well, where readers can put these methods into practice. Univariate Stable Distributions is ideal for advanced undergraduate or graduate students in mathematics, as well as many other fields, such as statistics, economics, engineering, physics, and more. It will also appeal to researchers in probability theory who seek an authoritative reference on stable distributions.



Theory of Distributions

Author : Svetlin G. Georgiev

Publisher : Springer

Page : 217 pages

File Size : 31,42 MB

Release : 2015-07-13

Category : Mathematics

ISBN : 3319195271

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Book Description

This book explains many fundamental ideas on the theory of distributions. The theory of partial differential equations is one of the synthetic branches of analysis that combines ideas and methods from different fields of mathematics, ranging from functional analysis and harmonic analysis to differential geometry and topology. This presents specific difficulties to those studying this field. This book, which consists of 10 chapters, is suitable for upper undergraduate/graduate students and mathematicians seeking an accessible introduction to some aspects of the theory of distributions. It can also be used for one-semester course.



Life Distributions

Author : Albert W. Marshall

Publisher : Springer Science & Business Media

Page : 785 pages

File Size : 40,73 MB

Release : 2007-10-13

Category : Technology & Engineering

ISBN : 0387684778

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Book Description

This book is devoted to the study of univariate distributions appropriate for the analyses of data known to be nonnegative. The book includes much material from reliability theory in engineering and survival analysis in medicine.



Extreme Value Distributions

Author : Samuel Kotz

Publisher : World Scientific

Page : 195 pages

File Size : 18,41 MB

Release : 2000

Category : Mathematics

ISBN : 1860944027

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Book Description

This important book provides an up-to-date comprehensive and down-to-earth survey of the theory and practice of extreme value distributions OCo one of the most prominent success stories of modern applied probability and statistics. Originated by E J Gumbel in the early forties as a tool for predicting floods, extreme value distributions evolved during the last 50 years into a coherent theory with applications in practically all fields of human endeavor where maximal or minimal values (the so-called extremes) are of relevance. The book is of usefulness both for a beginner with a limited probabilistic background and to expert in the field. Sample Chapter(s). Chapter 1.1: Historical Survey (139 KB). Chapter 1.2: The Three Types of Extreme Value Distributions (146 KB). Chapter 1.3: Limiting Distributions and Domain of Attraction (210 KB). Chapter 1.4: Distribution Function and Moments of Type 1 Distribution (160 KB). Chapter 1.5: Order Statistics, Record Values and Characterizations (175 KB). Contents: Univariate Extreme Value Distributions; Generalized Extreme Value Distributions; Multivariate Extreme Value Distributions. Readership: Applied probabilists, applied statisticians, environmental scientists, climatologists, industrial engineers and management experts."



Loss Distributions

Author : Robert V. Hogg

Publisher : John Wiley & Sons

Page : 254 pages

File Size : 50,15 MB

Release : 2009-09-25

Category : Business & Economics

ISBN : 0470317302

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Book Description

Devoted to the problem of fitting parametric probability distributions to data, this treatment uniquely unifies loss modeling in one book. Data sets used are related to the insurance industry, but can be applied to other distributions. Emphasis is on the distribution of single losses related to claims made against various types of insurance policies. Includes five sets of insurance data as examples.