Download or read book Characterization Problems Associated with the Exponential Distribution written by T. A. Azlarov and published by Springer. This book was released on 1986-05-09 with total page 152 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Characterization Problems Associated with the Exponential Distribution written by T. A. Azlarov and published by Springer. This book was released on 1986-05-23 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Characterizations of Probability Distributions written by Janos Galambos and published by Lecture Notes in Mathematics. This book was released on 1978-09 with total page 186 pages. Available in PDF, EPUB and Kindle. Book excerpt: Preliminaries and basic results; Characterizations based on truncated distributions; Characterizations by properties of order statistics; Characterization of the poisson process; Characterizations of multivariate exponential distributions.
Download or read book Exponential Distribution written by K. Balakrishnan and published by Routledge. This book was released on 2019-01-22 with total page 664 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Download or read book On a Characterization of the Exponential Distribution Based on a Type 2 Right Cesored Sample written by J. Leslie and published by . This book was released on 1991 with total page 17 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book A Characterization of the Exponential Distribution written by Thomas Shelburne Ferguson and published by . This book was released on 1963 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book On a Characterization of the Exponential Distribution written by M. Ahsanullah and published by . This book was released on 1975 with total page 10 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book On a Characterization of the Exponential Distribution by Order Statistics written by M. Ahsanullah and published by . This book was released on 1975 with total page 7 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Identifiability In Stochastic Models written by Bozzano G Luisa and published by Academic Press. This book was released on 2012-09-18 with total page 271 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Characterizations of Exponential Distribution by Ordered Random Variables written by Mohammad Ahsanullah and published by Nova Science Publishers. This book was released on 2019 with total page 192 pages. Available in PDF, EPUB and Kindle. Book excerpt: Exponential distribution is one of the most-used distributions in the theory and practice of statistics. It has several important properties like being memoryless and having a constant hazard rate. The field of characterization is developed in different branches of statistics and applied probability. Ordered random variables are common in various applications in practice. In this book, characterizations of exponential distribution using ordered random variables are presented. Most of the known results as well as many new results are given in this book. The aim of the book is to present various characterizations of exponential distribution based on ordered random variables. The book is written on a lower technical level and requires basic knowledge of mathematics and statistics. Chapter 1 gives some basic properties of exponential distribution. Chapters 2, 3, and 4 give the characterization of exponential distribution based on order statistics, record values, and generalized order statistics.
Download or read book On a characterization of the exponential distribution by properties of order statistics written by Ursula Gather and published by . This book was released on 1988 with total page 16 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book On a Characterization of the Exponential Distribution by Properties of Order Statistics written by U. Gather and published by . This book was released on 1988 with total page 8 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book A Characterization of Exponential Distributions Through Conditional Independence written by T. C. Liang and published by . This book was released on 1990 with total page 5 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Note on a Characterization of Exponential Distributions written by Samuel Kota and published by . This book was released on 1986 with total page 5 pages. Available in PDF, EPUB and Kindle. Book excerpt: This document shows that a certain relation is satisfied if and only if the components of Y are multiples of a single exponentially distributed random variable.
Download or read book Extreme Value Theory written by Jürg Hüsler and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 290 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Characterization of Geometric and Exponential Distributions written by Gordon B. Crawford and published by . This book was released on 1965 with total page 14 pages. Available in PDF, EPUB and Kindle. Book excerpt: In two works T.S. Ferguson examines the classes of independent random variables X and Y such that min(X, Y) is independent of X - Y. In one work he shows that if X (or Y) has a discrete part, then X and Y are geometric random variables. In the other work it is shown that if X and Y are absolutely continuous, then they are exponential random variables. The present author intends to complete this investigation by showing that the result of Ferguson holds even if X and Y are possibly singular.
Download or read book On a Characterization of the Exponential Distribution Based on a Type 2 Right Censored Sample written by Julian Leslie and published by . This book was released on 1991 with total page 17 pages. Available in PDF, EPUB and Kindle. Book excerpt:
