Marshall, Albert W.Overview
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Most widely held works by
Albert W Marshall
Inequalities : theory of majorization and its applications
by Albert W Marshall
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Book
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31 editions published between 1979 and 2011 in English and held by 1,033 WorldCat member libraries worldwide Statisticians, probabilists, and mathematicians will all be interested in a expanded version of this classic work on inequalities. The theory of inequalities has applications in virtually every branch of mathematics
Life distributions structure of nonparametric, semiparametric, and parametric families
by Albert W Marshall
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16 editions published between 2005 and 2011 in English and held by 538 WorldCat member libraries worldwide "For over 200 years, practitioners have been developing parametric families of probability distributions for data analysis. More recently, an active development of nonparametric and semiparametric families has occurred. This book includes an extensive discussion of a wide variety of distribution familiesnonparametric, semiparametric and parametricsome well known and some not. An allencompassing view is taken for the purpose of identifying relationships, origins, and structures of the various families. A unified methodological approach for the introduction of parameters into families is developed, and the properties that the parameters imbue a distribution are clarified. These results provide essential tools for intelligent choice of models for data analysis. Many of the results given are new and have not previously appeared in print. This book provides a comprehensive reference for anyone working with nonnegative data."Jacket
Apportionment of seats in proportional representation systems : a majorization comparison of divisor methods
by Albert W Marshall
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Book
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3 editions published in 1999 in English and held by 6 WorldCat member libraries worldwide
Neravenstva : teorija mažorizacii i ee priloženija; perevod s anglijskogo
by Albert W Marshall
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Book
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2 editions published in 1983 in Russian and held by 5 WorldCat member libraries worldwide
Multivariate Chebyshev type inequalities
by Albert W Marshall
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3 editions published in 1959 in English and held by 3 WorldCat member libraries worldwide
Chebyshev bounds for risks and error probabilities in some classification problems
by Stanford University
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Book
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3 editions published in 1969 in English and held by 3 WorldCat member libraries worldwide It is often the case that a random variable Y characterizes an item which is to be classified as belonging to one of several classes. When Y is expensive or impossible to observe, difficulties of classification arise and it may be desirable or necessary to classify the item on the basis of an auxiliary random variable X which is correlated with Y and may be regarded as a measure of Y. Of course, misclassification is a possibility. We assume that the loss suffered in such an event is determined by X and Y. When the joint distribution of X and Y is unknown, but only means, variances and covariance are known, the expected loss (risk) cannot be precisely computed. However, Chebyshevtype bounds for the risk can often be obtained for a given loss function. In this paper, several examples are presented which not only serve as illustrations, but which also are important in their own right. For certain kinds of classification procedures, bounds are also obtained for probabilities of misclassification. (Author)
A bivariate tchebycheff inequality for certain convex sets
by Albert W Marshall
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Book
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3 editions published in 1959 in English and held by 3 WorldCat member libraries worldwide
Tables of bounds for distributions with monotone hazard rate
by Richard E Barlow
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Book
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2 editions published in 1963 in English and held by 3 WorldCat member libraries worldwide A number of bounds for distributions with monotone hazard rate are presented in a form convenient for applications. These bounds, to gether with their proofs and various generaliza tions have been obtained by Barlow and Marshall (1963). However, many of them can be character ized only through solutions of transcendental equations, and machine calculation has been necessary to make them accessible. A listing of the results is given and those without ex plicit forms are tabulated. Various related bounds are listed which are of interest for purposes of comparison, and for use when the hypothesis of monotone hazard rate is bot satisfied. Applications of the bounds are dis cussed together with some numerical examples. (Author)
Neravenstva : teorii︠a︡ mazhorizat︠s︡ii i ee prilozhenii︠a︡
by Albert W Marshall
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Book
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2 editions published in 1983 in Russian and held by 3 WorldCat member libraries worldwide
Onesided inequalities of the Chebyshev type
by Albert W Marshall
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3 editions published in 1959 in English and held by 3 WorldCat member libraries worldwide Contents: Part 1  A onesided inequality of the Chebyshev type. Part 2  A onesided analog of Kolmogorov's inequality
A multivariate exponential distribution
by Albert W Marshall
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Book
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3 editions published in 1966 in English and held by 3 WorldCat member libraries worldwide A number of multivariate exponential distributions are known, but they have not been obtained by methods that shed light on their applicability. This paper presents some meaningful derivations of a multivariate exponential distribution that serve to indicate conditions under which the distribution is appropriate. Two of these derivations are based on 'shock models', and one is based on the requirement that residual life is independent of age. It is significant that the derivations all lead to the same distribution. For this distribution, the moment generating function is obtained, comparison is made with the case of independence, the distribution of the minimum is discussed, and various other properties are investigated. A multivariate gamma distribution is obtained by convolution, and a multivariate Weibull distribution is obtained through a change of variables. (Author)
Game theoretic proof that chebyshev inequalities are sharp
by Albert W Marshall
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Book
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3 editions published in 1960 in English and held by 3 WorldCat member libraries worldwide
Some inequalities for starshaped and convex functions
by Richard E Barlow
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Book
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2 editions published in 1967 in English and held by 3 WorldCat member libraries worldwide Necessary and sufficient conditons are obtained on a function G of bounded variation such that phi(integral sign x(t)dG(t)) = or <integral sign phi(x(t))dG(t) for all increasing x for which x(t sub 0) = 0 for some specified t sub 0, and all convex phi for which phi(0) = 0; the conditions are otherwise independent of phi and x. Similar results are obtained when the inequality is reversed. Necessary and sufficient conditions for both directions of inequality are also obtained when phi is starshaped. The relationship to previous results is sketched. Applications to statistical tolerance limits are indicated. (Author)
Enclosure theorems for eigenvalues and probability inequalities
by Albert W Marshall
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3 editions published in 1962 in English and held by 3 WorldCat member libraries worldwide
Matrix versions of the Cauchy and Kantorovich inequalities
by Stanford University
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Book
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3 editions published between 1987 and 1990 in English and held by 3 WorldCat member libraries worldwide
Monotonicity of ratios of means and other applications of majorization
by Albert W Marshall
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Book
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3 editions published in 1965 in English and held by 3 WorldCat member libraries worldwide Monotonicity of a ratio can be viewed as a form of total positivity. The theory of total positivity is exploited to obtain more general results. The proof of monotonicity is based on a theorem giving sufficient conditions for majorization. Several other applications of the majorization theorem are given. One application concerns a stochastic comparison between a function of order statistics from a distribution with increasing failure rate average and the same function of the order statistics from the exponential distribution. Another application is to a comparison between the condition number of a positive definite matrix and the condition number of a polynomial in the matrix
Multivariate exponential and geometric distributions with limited memory
by Stanford University
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2 editions published in 1994 in English and held by 2 WorldCat member libraries worldwide
Norms and inequalities for condition numbers, III
by Stanford University
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2 editions published in 1971 in English and held by 2 WorldCat member libraries worldwide
Neravenstva
by Albert W Marshall
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Book
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1 edition published in 1983 in Russian and held by 2 WorldCat member libraries worldwide
On the growth of stochastic processes
by Albert W Marshall
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Book
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2 editions published in 1958 in English and held by 2 WorldCat member libraries worldwide more
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Maršall, A.
Marshall, Albert
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