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Author: Tomasz J. Kozubowski
Publisher:
ISBN:
Category :
Languages : en
Pages : 0
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Consider a sum of independent and identically distributed random vectors with finite second moments, where the number of terms has a geometric distribution independent of the summands. We show that the class of limiting distributions of such random sums, as the number of terms converges to infinity, consists of multivariate asymmetric distributions that are natural generalizations of univariate Laplace laws. We call these limits multivariate asymmetric Laplace laws. We give an explicit form of their multidimensional densities and show representations that effectively facilitate computer simulation of variates from this class. We also discuss the relation to other formerly considered classes of distributions containing Laplace laws.
Author: Tomasz J. Kozubowski
Publisher:
ISBN:
Category :
Languages : en
Pages : 0
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Book Description
Consider a sum of independent and identically distributed random vectors with finite second moments, where the number of terms has a geometric distribution independent of the summands. We show that the class of limiting distributions of such random sums, as the number of terms converges to infinity, consists of multivariate asymmetric distributions that are natural generalizations of univariate Laplace laws. We call these limits multivariate asymmetric Laplace laws. We give an explicit form of their multidimensional densities and show representations that effectively facilitate computer simulation of variates from this class. We also discuss the relation to other formerly considered classes of distributions containing Laplace laws.
Author: Samuel Kotz
Publisher: Springer Science & Business Media
ISBN: 146120173X
Category : Mathematics
Languages : en
Pages : 358
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Book Description
This book describes the inferential and modeling advantages that this distribution, together with its generalizations and modifications, offers. The exposition systematically unfolds with many examples, tables, illustrations, and exercises. A comprehensive index and extensive bibliography also make this book an ideal text for a senior undergraduate and graduate seminar on statistical distributions, or for a short half-term academic course in statistics, applied probability, and finance.
Author: Tomasz J. Kozubowski
Publisher:
ISBN:
Category :
Languages : en
Pages : 28
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Author: Katarzyna Filipiak
Publisher: Springer Nature
ISBN: 3030754944
Category : Mathematics
Languages : en
Pages : 357
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Book Description
This book presents the latest findings on statistical inference in multivariate, multilinear and mixed linear models, providing a holistic presentation of the subject. It contains pioneering and carefully selected review contributions by experts in the field and guides the reader through topics related to estimation and testing of multivariate and mixed linear model parameters. Starting with the theory of multivariate distributions, covering identification and testing of covariance structures and means under various multivariate models, it goes on to discuss estimation in mixed linear models and their transformations. The results presented originate from the work of the research group Multivariate and Mixed Linear Models and their meetings held at the Mathematical Research and Conference Center in Będlewo, Poland, over the last 10 years. Featuring an extensive bibliography of related publications, the book is intended for PhD students and researchers in modern statistical science who are interested in multivariate and mixed linear models.
Author: Samuel Kotz
Publisher: World Scientific
ISBN: 9812561153
Category : Mathematics
Languages : en
Pages : 307
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Book Description
Statistical distributions are fundamental to Statistical Science and are a prime indispensable tool for its applications. This monograph is the first to examine an important but somewhat neglected field — univariate continuous distribution on a bounded domain, excluding the beta distribution. It provides an elementary but thorough discussion of “novel” contributions developed in recent years, such as the two-sided power, generalized trapezoidal and generalized Topp and Leone distributions, among others. It discusses a general framework for constructing two-sided distributions and some of its properties. It contains a comprehensive chapter on the triangular distribution as well as a chapter on earlier extensions not emphasized in existing literature. Special attention is given to estimation, in particular, non-standard maximum likelihood procedures. The applications are drawn mainly from the econometric and engineering domains.
Author: Brian Franczak
Publisher:
ISBN:
Category :
Languages : en
Pages :
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Author: Tomasz J. Kozubowski
Publisher:
ISBN:
Category :
Languages : en
Pages :
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Book Description
The generalized asymmetric Laplace (GAL) distribution, also known as the variance/mean-gamma model, is a popular flexible class of distributions that can account for peakedness, skewness, and heavier than normal tails, often observed in financial or other empirical data. We consider extensions of the GAL distribution to the matrix variate case, which arise as covariance mixtures of matrix variate normal distributions. Two different mixing mechanisms connected with the nature of the random scaling matrix are considered, leading to what we term matrix variate GAL distributions of Type I and II. While Type I matrix variate GAL distribution has been studied before, there is no comprehensive account of Type II in the literature, except for their rather brief treatment as a special case of matrix variate generalized hyperbolic distributions. With this work we fill this gap, and present an account for basic distributional properties of Type II matrix variate GAL distributions. In particular, we derive their probability density function and the characteristic function, as well as provide stochastic representations related to matrix variate gamma distribution. We also show that this distribution is closed under linear transformations, and study the relevant marginal distributions. In addition, we also briefly account for Type I and discuss the connections with Type II. We hope that this work will be useful in the areas where matrix variate distributions provide an appropriate probabilistic tool for three-way or, more generally, panel data sets, which can arise across different applications.
Author: Carles M. Cuadras
Publisher: Springer Science & Business Media
ISBN: 9401700613
Category : Mathematics
Languages : en
Pages : 252
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Book Description
This volume contains the papers presented at the meeting "Distributions with given marginals and statistical modelling", held in Barcelona (Spain), July 17- 20, 2000. This is the fourth meeting on given marginals, showing that this topic has aremarkable interest. BRIEF HISTORY The construction of distributions with given marginals started with the seminal papers by Hoeffding (1940) and Fn!chet (1951). Since then, many others have contributed on this topic: Dall' Aglio, Farlie, Gumbel, Johnson, Kellerer, Kotz, Morgenstern, Marshali, Olkin, Strassen, Vitale, Whitt, etc., as weIl as Arnold, Cambanis, Deheuvels, Genest, Frank, Joe, Kirneldorf, Nelsen, Rüschendorf, Sampson, Scarsini, Tiit, etc. In 1957 Sklar and Schweizer introduced probabilistic metric spaces. In 1975 Kirneldorf and Sampson studied the uniform representation of a bivariate dis tribution and proposed the desirable conditions that should be satisfied by any bivariate family. In 1991 Darsow, Nguyen and Olsen defined a natural operation between cop ulas, with applications in stochastic processes. In 1993, AIsina, Nelsen and Schweizer introduced the notion of quasi-copula
Author: Lev Borisovich Klebanov
Publisher: Nova Publishers
ISBN: 9781600212628
Category : Mathematics
Languages : en
Pages : 454
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Book Description
This volume is concerned with the problems in probability and statistics. Ill-posed problems are usually understood as those results where small changes in the assumptions lead to arbitrarily large changes in the conclusions. Such results are not very useful for practical applications where the presumptions usually hold only approximately (because even a slightest departure from the assumed model may produce an uncontrollable shift in the outcome). Often, the ill-posedness of certain practical problems is due to the lack of their precise mathematical formulation. Consequently, one can deal with such problems by replacing a given ill-posed problem with another, well-posed problem, which in some sense is 'close' to the original one. The goal in this book is to show that ill-posed problems are not just a mere curiosity in the contemporary theory of mathematical statistics and probability. On the contrary, such problems are quite common, and majority of classical results fall into this class. The objective of this book is to identify problems of this type, and re-formulate them more correctly. Thus, alternative (more precise in the above sense) versions are proposed of numerous classical theorems in the theory of probability and mathematical statistics. In addition, some non-standard problems are considered from this point of view.
Author: Samuel Kotz
Publisher:
ISBN: 9783764341664
Category :
Languages : en
Pages :
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