Download or read book Characterization of Matrix exponential Distributions written by Mark William Fackrell and published by . This book was released on 2003 with total page 402 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 Matrix Exponential Distributions in Applied Probability written by Mogens Bladt and published by Springer. This book was released on 2017-05-18 with total page 749 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains an in-depth treatment of matrix-exponential (ME) distributions and their sub-class of phase-type (PH) distributions. Loosely speaking, an ME distribution is obtained through replacing the intensity parameter in an exponential distribution by a matrix. The ME distributions can also be identified as the class of non-negative distributions with rational Laplace transforms. If the matrix has the structure of a sub-intensity matrix for a Markov jump process we obtain a PH distribution which allows for nice probabilistic interpretations facilitating the derivation of exact solutions and closed form formulas. The full potential of ME and PH unfolds in their use in stochastic modelling. Several chapters on generic applications, like renewal theory, random walks and regenerative processes, are included together with some specific examples from queueing theory and insurance risk. We emphasize our intention towards applications by including an extensive treatment on statistical methods for PH distributions and related processes that will allow practitioners to calibrate models to real data. Aimed as a textbook for graduate students in applied probability and statistics, the book provides all the necessary background on Poisson processes, Markov chains, jump processes, martingales and re-generative methods. It is our hope that the provided background may encourage researchers and practitioners from other fields, like biology, genetics and medicine, who wish to become acquainted with the matrix-exponential method and its applications.
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 Characterization of Distributions by the Method of Intensively Monotone Operators written by A.V. Kakosyan and published by Springer. This book was released on 2007-01-05 with total page 180 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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 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 Fundamentals of Matrix Analytic Methods written by Qi-Ming He and published by Springer Science & Business Media. This book was released on 2013-08-13 with total page 363 pages. Available in PDF, EPUB and Kindle. Book excerpt: Fundamentals of Matrix-Analytic Methods targets advanced-level students in mathematics, engineering and computer science. It focuses on the fundamental parts of Matrix-Analytic Methods, Phase-Type Distributions, Markovian arrival processes and Structured Markov chains and matrix geometric solutions. New materials and techniques are presented for the first time in research and engineering design. This book emphasizes stochastic modeling by offering probabilistic interpretation and constructive proofs for Matrix-Analytic Methods. Such an approach is especially useful for engineering analysis and design. Exercises and examples are provided throughout the book.
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 Matrix Analytic Methods in Stochastic Models written by Guy Latouche and published by Springer Science & Business Media. This book was released on 2012-12-04 with total page 265 pages. Available in PDF, EPUB and Kindle. Book excerpt: Matrix-analytic and related methods have become recognized as an important and fundamental approach for the mathematical analysis of general classes of complex stochastic models. Research in the area of matrix-analytic and related methods seeks to discover underlying probabilistic structures intrinsic in such stochastic models, develop numerical algorithms for computing functionals (e.g., performance measures) of the underlying stochastic processes, and apply these probabilistic structures and/or computational algorithms within a wide variety of fields. This volume presents recent research results on: the theory, algorithms and methodologies concerning matrix-analytic and related methods in stochastic models; and the application of matrix-analytic and related methods in various fields, which includes but is not limited to computer science and engineering, communication networks and telephony, electrical and industrial engineering, operations research, management science, financial and risk analysis, and bio-statistics. These research studies provide deep insights and understanding of the stochastic models of interest from a mathematics and/or applications perspective, as well as identify directions for future research.
Download or read book Exponentiated Distributions written by Essam K. AL-Hussaini and published by Springer. This book was released on 2015-01-06 with total page 149 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains entirely new results, not to be found elsewhere. Furthermore, additional results scattered elsewhere in the literature are clearly presented. Several well-known distributions such as Weibull distributions, exponentiated Burr type XII distributions and exponentiated exponential distributions and their properties are demonstrated. Analysis of real as well as well-simulated data are analyzed. A number of inferences based on a finite mixture of distributions are also presented.
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 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 Quantitative Assessments of Distributed Systems written by Dario Bruneo and published by John Wiley & Sons. This book was released on 2015-04-13 with total page 398 pages. Available in PDF, EPUB and Kindle. Book excerpt: Distributed systems employed in critical infrastructures must fulfill dependability, timeliness, and performance specifications. Since these systems most often operate in an unpredictable environment, their design and maintenance require quantitative evaluation of deterministic and probabilistic timed models. This need gave birth to an abundant literature devoted to formal modeling languages combined with analytical and simulative solution techniques The aim of the book is to provide an overview of techniques and methodologies dealing with such specific issues in the context of distributed systems and covering aspects such as performance evaluation, reliability/availability, energy efficiency, scalability, and sustainability. Specifically, techniques for checking and verifying if and how a distributed system satisfies the requirements, as well as how to properly evaluate non-functional aspects, or how to optimize the overall behavior of the system, are all discussed in the book. The scope has been selected to provide a thorough coverage on issues, models. and techniques relating to validation, evaluation and optimization of distributed systems. The key objective of this book is to help to bridge the gaps between modeling theory and the practice in distributed systems through specific examples.
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:
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:
