The Algebra Of Random Variables

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The Algebra Of Random Variables

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Author : Melvin Dale Springer
language : en
Publisher: John Wiley & Sons
Release Date : 1979

The Algebra Of Random Variables written by Melvin Dale Springer and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 1979 with Mathematics categories.

Differentiation and integration in the complex plane; The distribution of sums and differences of Random variables; The distribution of products and quotients of Random variables; The distribution of algebraic functions of independent Random variables; The distribution of algebraic functions of independent H-function variables; Analytical model for evaluation of the H-function inversion integral; Approximating the distribution of an algebraic function of independent random variables; Distribution problems in statistics.

Free Random Variables

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Author : Dan V. Voiculescu
language : en
Publisher: American Mathematical Soc.
Release Date : 1992

Free Random Variables written by Dan V. Voiculescu and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992 with Mathematics categories.

This book presents the first comprehensive introduction to free probability theory, a highly noncommutative probability theory with independence based on free products instead of tensor products. Basic examples of this kind of theory are provided by convolution operators on free groups and by the asymptotic behavior of large Gaussian random matrices. The probabilistic approach to free products has led to a recent surge of new results on the von Neumann algebras of free groups. The book is ideally suited as a textbook for an advanced graduate course and could also provide material for a seminar. In addition to researchers and graduate students in mathematics, this book will be of interest to physicists and others who use random matrices.

Sums Of Independent Random Variables

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Author : V.V. Petrov
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Sums Of Independent Random Variables written by V.V. Petrov and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.

The classic "Limit Dislribntions fOT slt1ns of Independent Ramdorn Vari ables" by B.V. Gnedenko and A.N. Kolmogorov was published in 1949. Since then the theory of summation of independent variables has devel oped rapidly. Today a summing-up of the studies in this area, and their results, would require many volumes. The monograph by I.A. Ibragi mov and Yu. V. I~innik, "Independent and Stationarily Connected VaTiables", which appeared in 1965, contains an exposition of the contem porary state of the theory of the summation of independent identically distributed random variables. The present book borders on that of Ibragimov and Linnik, sharing only a few common areas. Its main focus is on sums of independent but not necessarily identically distri buted random variables. It nevertheless includes a number of the most recent results relating to sums of independent and identically distributed variables. Together with limit theorems, it presents many probahilistic inequalities for sums of an arbitrary number of independent variables. The last two chapters deal with the laws of large numbers and the law of the iterated logarithm. These questions were not treated in Ibragimov and Linnik; Gnedenko and KolmogoTOv deals only with theorems on the weak law of large numbers. Thus this book may be taken as complementary to the book by Ibragimov and Linnik. I do not, however, assume that the reader is familiar with the latter, nor with the monograph by Gnedenko and Kolmogorov, which has long since become a bibliographical rarity

Random Variables

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Author : Lionel Edward Clarke
language : en
Publisher: Longman Publishing Group
Release Date : 1975

Random Variables written by Lionel Edward Clarke and has been published by Longman Publishing Group this book supported file pdf, txt, epub, kindle and other format this book has been release on 1975 with Mathematics categories.

Mixing Sequences Of Random Variables And Probabilistic Number Theory

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Author : Walter Philipp
language : en
Publisher: American Mathematical Soc.
Release Date : 1971

Mixing Sequences Of Random Variables And Probabilistic Number Theory written by Walter Philipp and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1971 with Additive functions categories.

The author gives a solution to the central limit problem and proves several forms of the iterated logarithm theorem and the results are then applied to the following branches of number theory: limit theorems for continued fractions and related algorithms; limit theorems in Diophantine approximations; discrepancies of sequences uniformly distributed mod one and the distribution of additive functions. In addition to new results, the major contribution of the work is the unification of the listed branches of probabilistic number theory. In particular, this is the first time that the distribution theory of additive functions has been related to metric number theory.

An Introduction To Algebraic Statistics With Tensors

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Author : Cristiano Bocci
language : en
Publisher: Springer Nature
Release Date : 2019-09-11

An Introduction To Algebraic Statistics With Tensors written by Cristiano Bocci and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-09-11 with Mathematics categories.

This book provides an introduction to various aspects of Algebraic Statistics with the principal aim of supporting Master’s and PhD students who wish to explore the algebraic point of view regarding recent developments in Statistics. The focus is on the background needed to explore the connections among discrete random variables. The main objects that encode these relations are multilinear matrices, i.e., tensors. The book aims to settle the basis of the correspondence between properties of tensors and their translation in Algebraic Geometry. It is divided into three parts, on Algebraic Statistics, Multilinear Algebra, and Algebraic Geometry. The primary purpose is to describe a bridge between the three theories, so that results and problems in one theory find a natural translation to the others. This task requires, from the statistical point of view, a rather unusual, but algebraically natural, presentation of random variables and their main classical features. The third part of the book can be considered as a short, almost self-contained, introduction to the basic concepts of algebraic varieties, which are part of the fundamental background for all who work in Algebraic Statistics.

Probability Algebras And Stochastic Spaces

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Author : Demetrios A. Kappos
language : en
Publisher: Academic Press
Release Date : 2014-07-03

Probability Algebras And Stochastic Spaces written by Demetrios A. Kappos and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-07-03 with Mathematics categories.

Probability Algebras and Stochastic Spaces explores the fundamental notions of probability theory in the so-called “point-free way. The space of all elementary random variables defined over a probability algebra in a “point-free way is a base for the stochastic space of all random variables, which can be obtained from it by lattice-theoretic extension processes. This book is composed of eight chapters and begins with discussions of the definition, properties, scope, and extension of probability algebras. The succeeding chapters deal with the Cartesian product of probability algebras and the principles of stochastic spaces. These topics are followed by surveys of the expectation, moments, and spaces of random variables. The final chapters define generalized random variables and the Boolean homomorphisms of these variables. This book will be of great value to mathematicians and advance mathematics students.

Random Variables On Boolean And Heyting Algebras And Their Numerical Characteristics

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Author : Ewa Rydzyńska
language : en
Publisher:
Release Date : 1990

Random Variables On Boolean And Heyting Algebras And Their Numerical Characteristics written by Ewa Rydzyńska and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1990 with Algebra, Boolean categories.

Some Algebra Of Independent Random Variables

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Author : Curtis White
language : en
Publisher:
Release Date : 2009

Some Algebra Of Independent Random Variables written by Curtis White and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009 with Random variables categories.

Free Random Variables

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Author : Dan V. Voiculescu
language : en
Publisher:
Release Date : 1992

Free Random Variables written by Dan V. Voiculescu and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992 with Free products categories.

This book presents the first comprehensive introduction to free probability theory, a highly noncommutative probability theory with independence based on free products instead of tensor products. Basic examples of this kind of theory are provided by convolution operators on free groups and by the asymptotic behavior of large Gaussian random matrices. The probabilistic approach to free products has led to a recent surge of new results on the von Neumann algebras of free groups. The book is ideally suited as a textbook for an advanced graduate course and could also provide material for a seminar.