Download or read book Characterizations of Mixtures of Exponential and Geometric Probability Distributions written by Manal Nassar and published by . This book was released on 1988 with total page 114 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Characterizations of Probability Distributions written by Janos Galambos and published by Springer. This book was released on 2006-11-15 with total page 177 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book On the Duality of Certain Characterizations of the Exponential and the Geometric Distributions written by John Panaretos and published by . This book was released on 2006 with total page 5 pages. Available in PDF, EPUB and Kindle. Book excerpt: Let {N(t), tgt;0} be a homogeneous Poisson process with parameter amp;λ=1. Let Z be a nonnegative random variable which is distributed independently of {N(t), tgt;0} according to a mixed game distribution. Xekalaki and Panaretos (1988) showed that the form of F (the mixing distribution) is uniquely determined by that of the distribution of N(Z). They also showed that certain characterizations of N(Z) can be derived through characterizations of F. In this paper it is demonstrated that through the above mentioned results a deeper insight is gained into the relationship of the distribution duals (geometric-exponential and Yule-Pareto). Two characterization theorems are also shown for the exponential distribution which can be thought of as variants of Govindarajulu's (1966) and Crawford's (1966) characterizations of the exponential distribution as the corresponding characterizing conditions are weaker than those used by them.
Download or read book Some Recent Characterizations of the Exponential and Geometric Distributions written by F. W. Steutel and published by . This book was released on 1990 with total page 12 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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 Characterizations of probability distributions written by János Galambos and published by . This book was released on 1978 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
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 Characterizations of Univariate Continuous Distributions written by Mohammad Ahsanullah and published by Springer. This book was released on 2017-04-18 with total page 130 pages. Available in PDF, EPUB and Kindle. Book excerpt: Provides in an organized manner characterizations of univariate probability distributions with many new results published in this area since the 1978 work of Golambos & Kotz "Characterizations of Probability Distributions" (Springer), together with applications of the theory in model fitting and predictions.
Download or read book Records via Probability Theory written by Mohammad Ahsanullah and published by Springer. This book was released on 2015-07-27 with total page 264 pages. Available in PDF, EPUB and Kindle. Book excerpt: A lot of statisticians, actuarial mathematicians, reliability engineers, meteorologists, hydrologists, economists. Business and sport analysts deal with records which play important roles in various fields of statistics and its application. This book enables a reader to check his/her level of understanding of the theory of record values. We give basic formulae which are more important in the theory and present a lot of examples which illustrate the theoretical statements. For a beginner in record statistics, as well as for graduate students the study of our book needs the basic knowledge of the subject. A more advanced reader can use our book to polish his/her knowledge. An upgraded list of bibliography which will help a reader to enrich his/her theoretical knowledge and widen the experience of dealing with ordered observations, is also given in the book.
Download or read book A Note on the Characterization of Exponential and Geometric Distributions written by Yoon-Kwai Leong and published by . This book was released on 1979 with total page 10 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Recent Results on Characterization of Probability Distributions a Unified Approach Through Extensions of Deny s Theorem written by University of Pittsburgh. Center for Multivariate Analysis and published by . This book was released on 1984 with total page 35 pages. Available in PDF, EPUB and Kindle. Book excerpt: The problem of identifying solutions of general convolution equations relative to a group has been studied in two classical papers by Choquet and Deny. Recently, Lau and Rao have considered the analogous problem relative to a certain semigroup of the real line, which extends the results of Marsaglia and Tubilla and a lemma of Shanbhag. The extended versions of Deny's theorem contained in the papers by Lau and Rao, and Shanbhag (which referred to as LRS theorems) yield as special cases improved versions of several characterizations of exponential, Weibull, stable, Pareto, geometric, Poisson and negative binomial distributions obtained by various authors during the last few years. This paper reviews some of the recent contributions to characterization of probability distributions (whose authors do not seem to be aware of LRS theorems or special cases existing earlier) and show how improved versions of these results follow as immediate corollaries to LRS theorems. It also gives a short proof of Lau-Rao theorem based on Deny's theorem and thus establish a direct link between the results of Deny and those of Lau and Rao. A variant of Lau-Rao theorem is proved and applied to some characterization problems.
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 Exponential Distribution written by K. Balakrishnan and published by CRC Press. This book was released on 1996-02-07 with total page 668 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 exponential distribution. Discussions include exponential regression, models and applications of mixtures, and applications to survival analysis.
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 Finite Mixture Distributions written by B. Everitt and published by Springer. This book was released on 1981-05-28 with total page 160 pages. Available in PDF, EPUB and Kindle. Book excerpt: General introduction; Mixtures of normal distributions; Mixtures of exponential and other continuous distributions; Mixtures of discrete distributions; Miscellaneous topics.
Download or read book Probability Distributions Used in Reliability Engineering written by Andrew N O'Connor and published by RIAC. This book was released on 2011 with total page 220 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book provides details on 22 probability distributions. Each distribution section provides a graphical visualization and formulas for distribution parameters, along with distribution formulas. Common statistics such as moments and percentile formulas are followed by likelihood functions and in many cases the derivation of maximum likelihood estimates. Bayesian non-informative and conjugate priors are provided followed by a discussion on the distribution characteristics and applications in reliability engineering.
Download or read book Characterizations of Probability Distributions written by Janos Galambos and published by . This book was released on 2014-09-01 with total page 180 pages. Available in PDF, EPUB and Kindle. Book excerpt:
