Stochastic Comparisons with Applications
Stochastic Comparisons with Applications

Author: Subhash C. Kochar

Publisher: Springer Nature

Published: 2022-10-22

Total Pages: 280

ISBN-13: 303112104X

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This book emphasizes the use of stochastic orders as motivational tools for developing new statistical procedures. Stochastic orders have found useful applications in many disciplines, including reliability theory, survival analysis, risk theory, finance, nonparametric methods, economics and actuarial science. Written by a statistician, this volume clarifies the connection between stochastic orders and nonparametric methods. The importance of order statistics and spacings is well recognized. Classically, they mainly focus on the case when the observations are independent and identically distributed, however, several new developments have extended the comparison of order statistics to the case of non-identically distributed or non-independent observations. In addition to giving a detailed discussion of various topics in the general area of stochastic orders, a substantial part of the book is devoted to recent research on stochastic comparisons of order statistics and spacings, including a long chapter on dependence among them. The book will be useful for graduate students and researchers in statistics, economics, actuarial science and other related disciplines. In particular, with close to 300 references, it will be a valuable resource for reliability theorists, applied probabilists and statisticians. Readers are expected to have taken a first-year graduate level course in mathematical statistics or in applied probability.

Comparisons of Stochastic Matrices with Applications in Information Theory, Statistics, Economics and Population
Comparisons of Stochastic Matrices with Applications in Information Theory, Statistics, Economics and Population

Author: JOEL COHEN

Publisher: Springer Science & Business Media

Published: 1998-09-29

Total Pages: 170

ISBN-13: 9780817640828

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Some of the possible implications among these comparisons remain open questions. The results in this book establish a new field of investigation for both mathematicians and scientific users interested in the variations among multiple probability distributions.

Stochastic Orders in Reliability and Risk
Stochastic Orders in Reliability and Risk

Author: Haijun Li

Publisher: Springer Science & Business Media

Published: 2013-06-22

Total Pages: 459

ISBN-13: 1461468922

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Stochastic Orders in Reliability and Risk Management is composed of 19 contributions on the theory of stochastic orders, stochastic comparison of order statistics, stochastic orders in reliability and risk analysis, and applications. These review/exploratory chapters present recent and current research on stochastic orders reported at the International Workshop on Stochastic Orders in Reliability and Risk Management, or SORR2011, which took place in the City Hotel, Xiamen, China, from June 27 to June 29, 2011. The conference’s talks and invited contributions also represent the celebration of Professor Moshe Shaked, who has made comprehensive, fundamental contributions to the theory of stochastic orders and its applications in reliability, queueing modeling, operations research, economics and risk analysis. This volume is in honor of Professor Moshe Shaked. The work presented in this volume represents active research on stochastic orders and multivariate dependence, and exemplifies close collaborations between scholars working in different fields. The Xiamen Workshop and this volume seek to revive the community workshop tradition on stochastic orders and dependence and strengthen research collaboration, while honoring the work of a distinguished scholar.

An Introduction to Stochastic Orders
An Introduction to Stochastic Orders

Author: Felix Belzunce

Publisher: Academic Press

Published: 2015-09-29

Total Pages: 175

ISBN-13: 0128038268

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An Introduction to Stochastic Orders discusses this powerful tool that can be used in comparing probabilistic models in different areas such as reliability, survival analysis, risks, finance, and economics. The book provides a general background on this topic for students and researchers who want to use it as a tool for their research. In addition, users will find detailed proofs of the main results and applications to several probabilistic models of interest in several fields, and discussions of fundamental properties of several stochastic orders, in the univariate and multivariate cases, along with applications to probabilistic models. Introduces stochastic orders and its notation Discusses different orders of univariate stochastic orders Explains multivariate stochastic orders and their convex, likelihood ratio, and dispersive orders

Stochastic Orders and Their Applications
Stochastic Orders and Their Applications

Author: Moshe Shaked

Publisher:

Published: 1994

Total Pages: 580

ISBN-13:

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Stochastic orders and inequalities are being used at an accelerated rate in many diverse areas of probability and statistics. This book provides the first unified, systematic, and accessible treatment of stochasticorders, addressing the growing importance of these orders with the presentation of numerous results that illustrate their usefulness and applicability. Ten insightful chapters emphasize the applications by specialists in probability and statistics, economics, operations research, and reliability theory. Applications include multivariate variability, epidemics, comparisons of risk and risk aversion, scheduling, and systems reliability theory.

Stochastic Comparisons of Order Statistics, with Applications in Reliability
Stochastic Comparisons of Order Statistics, with Applications in Reliability

Author: Jee S. Kim

Publisher:

Published: 1987

Total Pages: 19

ISBN-13:

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This paper surveys recent advances in stochastic comparisons of order statistics along with reliability applications. Section 2 presents inequalities for linear combinations of order statistics from restricted families. Comparisons of linear combinations of order statistics from distributions F and G are obtained for/G F convex and for/G F starshaped. These results yield conservative upper and lower tolerance limits. For G exponential and F IFR or IFRA, stochastic comparisons are presented for the total time on test, used in life testing. Section 3 presents stochastic comparisons of order statistics from underlying heterogeneous distributions. Given two sets of independent components (possibly unlike), majorization conditions are given which insure that any k-out-of-n system constructed from components in the first set will have reliability at least as great as that of a corresponding system constructed from components in the second set. Since the ordered failure times of the components represent order statistics from heterogeneous distributions, the order statistics from one set of underlying distributions (F1, ..., Fn) can be compared stochastically with those from another set (F1, ..., Fn).

Stochastic Comparisons of Order Statistics from Heterogeneous Populations, with Applications in Reliability
Stochastic Comparisons of Order Statistics from Heterogeneous Populations, with Applications in Reliability

Author: F. Proschan

Publisher:

Published: 1975

Total Pages: 19

ISBN-13:

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In this paper, the authors stochastically compare whole vectors of order statistics. This stochastic vector comparison yields as special cases a number of previous results such as the Pledger-Proschan results and additional results stochastically comparing partial or complete sums of order statistics. It is shown that some of these results concerning stochastic comparison of sums remain valid if one does not order the sample, but instead uses the ordering specified by the constants of proportionality of the hazard functions.

Stochastic Processes
Stochastic Processes

Author: Pierre Del Moral

Publisher: CRC Press

Published: 2017-02-24

Total Pages: 866

ISBN-13: 1498701841

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Unlike traditional books presenting stochastic processes in an academic way, this book includes concrete applications that students will find interesting such as gambling, finance, physics, signal processing, statistics, fractals, and biology. Written with an important illustrated guide in the beginning, it contains many illustrations, photos and pictures, along with several website links. Computational tools such as simulation and Monte Carlo methods are included as well as complete toolboxes for both traditional and new computational techniques.

Stochastic Processes and Their Applications
Stochastic Processes and Their Applications

Author: Frank Beichelt

Publisher: CRC Press

Published: 2001-10-18

Total Pages: 342

ISBN-13: 9780415272322

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This book introduces stochastic processes and their applications for students in engineering, industrial statistics, science, operations research, business, and finance. It provides the theoretical foundations for modeling time-dependent random phenomena encountered in these disciplines. Through numerous science and engineering-based examples and exercises, the author presents the subject in a comprehensible, practically oriented way, but he also includes some important proofs and theoretically challenging examples and exercises that will appeal to more mathematically minded readers. Solutions to most of the exercises are included either in an appendix or within the text.

Frontiers in Reliability
Frontiers in Reliability

Author: Asit P. Basu

Publisher: World Scientific

Published: 1998

Total Pages: 512

ISBN-13: 9789810233600

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This volume presents recent results in reliability theory by leading experts in the world. It will prove valuable for researchers, and users of reliability theory. It consists of refereed invited papers on a broad spectrum of topics in reliability. The subjects covered include Bayesian reliability, Bayesian reliability modeling, confounding in a series system, DF tests, Edgeworth approximation to reliability, estimation under random censoring, fault tree reduction for reliability, inference about changes in hazard rates, information theory and reliability, mixture experiment, mixture of Weibull distributions, queuing network approach in reliability theory, reliability estimation, reliability modeling, repairable systems, residual life function, software spare allocation systems, stochastic comparisons, stress-strength models, system-based component test plans, and TTT-transform.