Characterization Problems Associated With The Exponential Distribution

Author : T. A. Azlarov,N. A. Volodin
Publisher : Springer
Page : 152 pages
File Size : 49,6 Mb
Release : 1986-05-09
Category : Mathematics
ISBN : STANFORD:36105032330818

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Characterization Problems Associated with the Exponential Distribution by T. A. Azlarov,N. A. Volodin Pdf

Problems of calculating the reliability of instruments and systems and the development of measures to increase efficiency and reduce operational costs confronted physicists and mathe maticians at the end of the '40's and the beginning of the '50's in connection with the unrelia bility of electro-vacuum instruments used in aviation. Since then steadily increasing demands for the accuracy, reliability and complexity required in electronic equipment have served as a stimulus in the development of the theory of reliability. From 1950 to 1955 Epstein and Sobel [67,68] and Davis [62], in an analysis of statistical data of the operating time of an instrument up to failure, showed that the distribution is exponential in many cases. Consequently, the ex ponential distribution became basic to research associated with experiments on life expectancy. Further research has shown that there are a whole series of problems in reliability theory for which the exponential distribution is inapplicable. However, it can practically always be used as a first approximation. The ease of computational work due to the nice properties of the exponential distribution (for example, the lack of memory property, see Section 1) is also a reason for its frequent use. AB a rule, data on the behavior of the failure rate function are used to test the hypothesis that a given distribution belongs to the class of exponential distributions, and order statistics are used to estimate the parameter of the exponential distribution.

Author : T. A. Azlarov,N. A. Volodin
Publisher : Springer
Page : 0 pages
File Size : 49,6 Mb
Release : 1986-05-23
Category : Mathematics
ISBN : 1461249562

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Characterization Problems Associated with the Exponential Distribution by T. A. Azlarov,N. A. Volodin Pdf

Problems of calculating the reliability of instruments and systems and the development of measures to increase efficiency and reduce operational costs confronted physicists and mathe maticians at the end of the '40's and the beginning of the '50's in connection with the unrelia bility of electro-vacuum instruments used in aviation. Since then steadily increasing demands for the accuracy, reliability and complexity required in electronic equipment have served as a stimulus in the development of the theory of reliability. From 1950 to 1955 Epstein and Sobel [67,68] and Davis [62], in an analysis of statistical data of the operating time of an instrument up to failure, showed that the distribution is exponential in many cases. Consequently, the ex ponential distribution became basic to research associated with experiments on life expectancy. Further research has shown that there are a whole series of problems in reliability theory for which the exponential distribution is inapplicable. However, it can practically always be used as a first approximation. The ease of computational work due to the nice properties of the exponential distribution (for example, the lack of memory property, see Section 1) is also a reason for its frequent use. AB a rule, data on the behavior of the failure rate function are used to test the hypothesis that a given distribution belongs to the class of exponential distributions, and order statistics are used to estimate the parameter of the exponential distribution.

Author : Janos Galambos,Samuel Kotz
Publisher : Springer
Page : 177 pages
File Size : 46,7 Mb
Release : 2006-11-15
Category : Mathematics
ISBN : 9783540357339

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Characterizations of Probability Distributions. by Janos Galambos,Samuel Kotz Pdf

Author : K. Balakrishnan
Publisher : Routledge
Page : 664 pages
File Size : 51,5 Mb
Release : 2019-01-22
Category : Mathematics
ISBN : 9781351449120

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Exponential Distribution by K. Balakrishnan Pdf

The exponential distribution is one of the most significant and widely used distribution in statistical practice. It possesses several important statistical properties, and yet exhibits great mathematical tractability. This volume provides a systematic and comprehensive synthesis of the diverse literature on the theory and applications of the expon

Author : K. Balakrishnan
Publisher : Routledge
Page : 414 pages
File Size : 55,6 Mb
Release : 2019-01-22
Category : Mathematics
ISBN : 9781351449113

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Exponential Distribution by K. Balakrishnan Pdf

The exponential distribution is one of the most significant and widely used distribution in statistical practice. It possesses several important statistical properties, and yet exhibits great mathematical tractability. This volume provides a systematic and comprehensive synthesis of the diverse literature on the theory and applications of the expon

Author : Jürg Hüsler,Rolf-Dieter Reiss
Publisher : Springer Science & Business Media
Page : 290 pages
File Size : 44,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461236344

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Extreme Value Theory by Jürg Hüsler,Rolf-Dieter Reiss Pdf

The urgent need to describe and to solve certain problems connected to extreme phenomena in various areas of applications has been of decisive influence on the vital development of extreme value theory. After the pioneering work of M. Frechet (1927) and of R.A. Fisher and L.R.C. Tippett (1928), who discovered the limiting distributions of extremes, the importance of mathematical concepts of extreme behavior in applications was impressively demonstrated by statisticians like E.J. Gumbel and W. Weibull. The predominant role of applied aspects in that early period may be highlighted by the fact that two of the "Fisher-Tippett asymptotes" also carry the names of Gumbel and Weibull. In the last years, the complexity of problems and their tractability by mathematical methods stimulated a rapid development of mathematical theory that substantially helped to improve our understanding of extreme behavior. Due to the depth and richness of mathematical ideas, extreme value theory has become more and more of interest for mathematically oriented research workers. This was one of the reasons to organize a conference on extreme value theory which was held at the Mathematische Forschungsinstitut at Oberwolfach (FRG) in December 1987.

Author : N. Balakrishnan
Publisher : CRC Press
Page : 624 pages
File Size : 43,8 Mb
Release : 1991-11-27
Category : Mathematics
ISBN : 9781482277098

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Handbook of the Logistic Distribution by N. Balakrishnan Pdf

This book highlights various theoretical developments on logistic distribution, illustrates the practical utility of these results, and describes univariate and multivariate generalizations of the distribution. It is useful for researchers, practicing statisticians, and graduate students.

Author : Mohammad Ahsanullah
Publisher : Springer
Page : 137 pages
File Size : 43,6 Mb
Release : 2016-09-15
Category : Mathematics
ISBN : 9789462392229

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Extreme Value Distributions by Mohammad Ahsanullah Pdf

The aim of the book is to give a through account of the basic theory of extreme value distributions. The book cover a wide range of materials available to date. The central ideas and results of extreme value distributions are presented. The book rwill be useful o applied statisticians as well statisticians interrested to work in the area of extremen value distributions.vmonograph presents the central ideas and results of extreme value distributions.The monograph gives self-contained of theory and applications of extreme value distributions.

Author : Kai Wang Fang
Publisher : CRC Press
Page : 126 pages
File Size : 54,5 Mb
Release : 2018-01-18
Category : Mathematics
ISBN : 9781351093941

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Symmetric Multivariate and Related Distributions by Kai Wang Fang Pdf

Since the publication of the by now classical Johnson and Kotz Continuous Multivariate Distributions (Wiley, 1972) there have been substantial developments in multivariate distribution theory especially in the area of non-normal symmetric multivariate distributions. The book by Fang, Kotz and Ng summarizes these developments in a manner which is accessible to a reader with only limited background (advanced real-analysis calculus, linear algebra and elementary matrix calculus). Many of the results in this field are due to Kai-Tai Fang and his associates and appeared in Chinese publications only. A thorough literature search was conducted and the book represents the latest work - as of 1988 - in this rapidly developing field of multivariate distributions. The authors are experts in statistical distribution theory.

Author : Mohammad Ahsanullah,Valeriĭ Borisovich Nevzorov
Publisher : Nova Publishers
Page : 252 pages
File Size : 50,5 Mb
Release : 2005
Category : Mathematics
ISBN : 1594540713

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Order Statistics by Mohammad Ahsanullah,Valeriĭ Borisovich Nevzorov Pdf

A lot of probabilists and statisticians, as well as actuarial mathematicians, reliability engineers, meteorologists, hydrologists, economists, business and sport analysts, very often deal with order statistics, which plays an important role in various fields of statistics and its applications. The authors suggest an approach to studying order statistics which proposes an active participation of our reader in the studying process. This book enables a reader to check his/her level of understanding of the theory of order statistics. It gives basic formulae (without proof), which are most important in the theory, and presents a lot of examples, which illustrate the theoretical statements.

Author : M. Ataharul Islam,Rafiqul I Chowdhury
Publisher : Springer
Page : 250 pages
File Size : 52,7 Mb
Release : 2017-07-06
Category : Business & Economics
ISBN : 9789811037948

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Analysis of Repeated Measures Data by M. Ataharul Islam,Rafiqul I Chowdhury Pdf

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.

Author : Mohammad Ahsanullah
Publisher : University Press of America
Page : 326 pages
File Size : 43,9 Mb
Release : 2004
Category : Business & Economics
ISBN : 0761827943

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Record Values--theory and Applications by Mohammad Ahsanullah Pdf

In this book, Mohammad Ahsanullah provides a detailed description of the general theory and applications of record values. Professor Ahsanullah thoroughly discusses the most useful distributions and inferences based on record values, resulting in conclusions that are not available in previously published works.

Author : Albert Tarantola
Publisher : SIAM
Page : 348 pages
File Size : 54,6 Mb
Release : 2005-01-01
Category : Mathematics
ISBN : 9780898715729

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Inverse Problem Theory and Methods for Model Parameter Estimation by Albert Tarantola Pdf

This book proposes a general approach to the basic difficulties appearing in the resolution of inverse problems.

Author : Bozzano G Luisa
Publisher : Academic Press
Page : 271 pages
File Size : 43,8 Mb
Release : 2012-09-18
Category : Mathematics
ISBN : 9780128015261

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Identifiability In Stochastic Models by Bozzano G Luisa Pdf

The problem of identifiability is basic to all statistical methods and data analysis, occurring in such diverse areas as Reliability Theory, Survival Analysis, and Econometrics, where stochastic modeling is widely used. Mathematics dealing with identifiability per se is closely related to the so-called branch of "characterization problems" in Probability Theory. This book brings together relevant material on identifiability as it occurs in these diverse fields.

Author : Barry C. Arnold,Narayanaswamy Balakrishnan,Haikady N. Nagaraja
Publisher : John Wiley & Sons
Page : 342 pages
File Size : 44,9 Mb
Release : 2011-09-20
Category : Mathematics
ISBN : 9781118150405

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Records by Barry C. Arnold,Narayanaswamy Balakrishnan,Haikady N. Nagaraja Pdf

The first and only comprehensive guide to modern record theory andits applications Although it is often thought of as a special topic in orderstatistics, records form a unique area, independent of the study ofsample extremes. Interest in records has increased steadily overthe years since Chandler formulated the theory of records in 1952.Numerous applications of them have been developed in such far-flungfields as meteorology, sports analysis, hydrology, and stock marketanalysis, to name just a few. And the literature on the subjectcurrently comprises papers and journal articles numbering in thehundreds. Which is why it is so nice to have this book devotedexclusively to this lively area of statistics. Written by an exceptionally well-qualified author team, Recordspresents a comprehensive treatment of record theory and itsapplications in a variety of disciplines. With the help of amultitude of fascinating examples, Professors Arnold, Balakrishnan,and Nagaraja help readers quickly master basic and advanced recordvalue concepts and procedures, from the classical record valuemodel to random and multivariate record models. The book follows arational textbook format, featuring witty and insightful chapterintroductions that help smooth transitions from one topic toanother and challenging chapter-end exercises, which expand on thematerial covered. An extensive bibliography and numerous referencesthroughout the text specify sources for further readings onrelevant topics. Records is a valuable professional resource forprobabilists and statisticians, in addition to appliedstatisticians, meteorologists, hydrologists, market analysts, andsports analysts. It also makes an excellent primary text forcourses in record theory and a supplement to order statisticscourses.