[PDF] Finding An H Function Distribution For The Sum Of Independent H Function Variates eBook

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Publisher :
Page : 243 pages
File Size : 20,40 MB
Release : 1981
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A practical technique is presented for determining the exact probability density function and cumulative distribution function of a sum of any number of terms involving any combination of products, quotients, and powers of independent random variables with H-function distributions. The H-function is the most general named function, encompassing as special cases most of the other special functions of mathematics and many of the classical statistical distributions. Its unique properties make it a powerful tool for statistical analysis. In particular, the product, quotient, and powers of independent H- function variates are also H-function variates, and the Laplace and Fourier transforms and the derivatives of an H-function are readily-determined H- functions. This dissertation provides background material, including history on H-functions and the algebra of random variables and definition, properties and special cases of the H-function. For determining whether convergence of a general Mellin-Barnes integral or an H-function occurs with left-half-plane versus right-half-plane summation of residues, evaluation guidelines are formally established and applied to the known special cases, the Laplace transform, and the derivatives of the H-function. Then, a new, improved formulation for evaluation of an H-function by summing residues is derived.

Author : W. Jackson Hall
Publisher : CRC Press
Page : 330 pages
File Size : 32,60 MB
Release : 2023-12-14
Category : Mathematics
ISBN : 1498726119

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This book provides an accessible but rigorous introduction to asymptotic theory in parametric statistical models. Asymptotic results for estimation and testing are derived using the “moving alternative” formulation due to R. A. Fisher and L. Le Cam. Later chapters include discussions of linear rank statistics and of chi-squared tests for contingency table analysis, including situations where parameters are estimated from the complete ungrouped data. This book is based on lecture notes prepared by the first author, subsequently edited, expanded and updated by the second author. Key features: • Succinct account of the concept of “asymptotic linearity” and its uses • Simplified derivations of the major results, under an assumption of joint asymptotic normality • Inclusion of numerical illustrations, practical examples and advice • Highlighting some unexpected consequences of the theory • Large number of exercises, many with hints to solutions Some facility with linear algebra and with real analysis including ‘epsilon-delta’ arguments is required. Concepts and results from measure theory are explained when used. Familiarity with undergraduate probability and statistics including basic concepts of estimation and hypothesis testing is necessary, and experience with applying these concepts to data analysis would be very helpful.

Author : E. S. Keeping
Publisher : Courier Corporation
Page : 484 pages
File Size : 12,4 MB
Release : 1995-01-01
Category : Mathematics
ISBN : 9780486685021

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This excellent text emphasizes the inferential and decision-making aspects of statistics. The first chapter is mainly concerned with the elements of the calculus of probability. Additional chapters cover the general properties of distributions, testing hypotheses, and more.

Author : V. S. Pugachev
Publisher : Elsevier
Page : 469 pages
File Size : 31,94 MB
Release : 2014-06-28
Category : Mathematics
ISBN : 1483190501

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Probability Theory and Mathematical Statistics for Engineers focuses on the concepts of probability theory and mathematical statistics for finite-dimensional random variables. The book underscores the probabilities of events, random variables, and numerical characteristics of random variables. Discussions focus on canonical expansions of random vectors, second-order moments of random vectors, generalization of the density concept, entropy of a distribution, direct evaluation of probabilities, and conditional probabilities. The text then examines projections of random vectors and their distributions, including conditional distributions of projections of a random vector, conditional numerical characteristics, and information contained in random variables. The book elaborates on the functions of random variables and estimation of parameters of distributions. Topics include frequency as a probability estimate, estimation of statistical characteristics, estimation of the expectation and covariance matrix of a random vector, and testing the hypotheses on the parameters of distributions. The text then takes a look at estimator theory and estimation of distributions. The book is a vital source of data for students, engineers, postgraduates of applied mathematics, and other institutes of higher technical education.

Author : V Berdichevsky
Publisher : CRC Press
Page : 282 pages
File Size : 31,43 MB
Release : 1997-10-24
Category : Science
ISBN : 9780582087347

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The discovery of chaotic motion in low-dimensional systems raised the question: What kind of thermodynamics describes a system if it is neither ergodic nor Hamiltonian or possesses a finite number of degrees of freedom? This Monographs is the first to discuss this question.