[PDF] Evaluation Of The H Function Integral And Of Probability Distributions Of Functions Of Independent Random Variables eBook

Author :
Publisher :
Page : 243 pages
File Size : 26,31 MB
Release : 1981
Category :
ISBN :

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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 : Thu Pham-gia
Publisher : World Scientific
Page : 494 pages
File Size : 12,66 MB
Release : 2021-05-05
Category : Business & Economics
ISBN : 9811235309

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This book provides the reader with user-friendly applications of normal distribution. In several variables it is called the multinormal distribution which is often handled using matrices for convenience. The author seeks to make the arguments less abstract and hence, starts with the univariate case and moves progressively toward the vector and matrix cases. The approach used in the book is a gradual one, going from one scalar variable to a vector variable and to a matrix variable. The author presents the unified aspect of normal distribution, as well as addresses several other issues, including random matrix theory in physics. Other well-known applications, such as Herrnstein and Murray's argument that human intelligence is substantially influenced by both inherited and environmental factors, will be discussed in this book. It is a better predictor of many personal dynamics — including financial income, job performance, birth out of wedlock, and involvement in crime — than are an individual's parental socioeconomic status, or education level, and deserve to be mentioned and discussed.

Author : A.M. Mathai
Publisher : Springer Science & Business Media
Page : 276 pages
File Size : 34,42 MB
Release : 2009-10-10
Category : Science
ISBN : 1441909168

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TheH-function or popularly known in the literature as Fox’sH-function has recently found applications in a large variety of problems connected with reaction, diffusion, reaction–diffusion, engineering and communication, fractional differ- tial and integral equations, many areas of theoretical physics, statistical distribution theory, etc. One of the standard books and most cited book on the topic is the 1978 book of Mathai and Saxena. Since then, the subject has grown a lot, mainly in the elds of applications. Due to popular demand, the authors were requested to - grade and bring out a revised edition of the 1978 book. It was decided to bring out a new book, mostly dealing with recent applications in statistical distributions, pa- way models, nonextensive statistical mechanics, astrophysics problems, fractional calculus, etc. and to make use of the expertise of Hans J. Haubold in astrophysics area also. It was decided to con ne the discussion toH-function of one scalar variable only. Matrix variable cases and many variable cases are not discussed in detail, but an insight into these areas is given. When going from one variable to many variables, there is nothing called a unique bivariate or multivariate analogue of a givenfunction. Whatever be the criteria used, there may be manydifferentfunctions quali ed to be bivariate or multivariate analogues of a given univariate function. Some of the bivariate and multivariateH-functions, currently in the literature, are also questioned by many authors.

Author : Houshang H. Sohrab
Publisher : Springer
Page : 687 pages
File Size : 24,1 MB
Release : 2014-11-15
Category : Mathematics
ISBN : 1493918419

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This expanded second edition presents the fundamentals and touchstone results of real analysis in full rigor, but in a style that requires little prior familiarity with proofs or mathematical language. The text is a comprehensive and largely self-contained introduction to the theory of real-valued functions of a real variable. The chapters on Lebesgue measure and integral have been rewritten entirely and greatly improved. They now contain Lebesgue’s differentiation theorem as well as his versions of the Fundamental Theorem(s) of Calculus. With expanded chapters, additional problems, and an expansive solutions manual, Basic Real Analysis, Second Edition is ideal for senior undergraduates and first-year graduate students, both as a classroom text and a self-study guide. Reviews of first edition: The book is a clear and well-structured introduction to real analysis aimed at senior undergraduate and beginning graduate students. The prerequisites are few, but a certain mathematical sophistication is required. ... The text contains carefully worked out examples which contribute motivating and helping to understand the theory. There is also an excellent selection of exercises within the text and problem sections at the end of each chapter. In fact, this textbook can serve as a source of examples and exercises in real analysis. —Zentralblatt MATH The quality of the exposition is good: strong and complete versions of theorems are preferred, and the material is organised so that all the proofs are of easily manageable length; motivational comments are helpful, and there are plenty of illustrative examples. The reader is strongly encouraged to learn by doing: exercises are sprinkled liberally throughout the text and each chapter ends with a set of problems, about 650 in all, some of which are of considerable intrinsic interest. —Mathematical Reviews [This text] introduces upper-division undergraduate or first-year graduate students to real analysis.... Problems and exercises abound; an appendix constructs the reals as the Cauchy (sequential) completion of the rationals; references are copious and judiciously chosen; and a detailed index brings up the rear. —CHOICE Reviews

Author : Melvin Dale Springer
Publisher : John Wiley & Sons
Page : 510 pages
File Size : 47,37 MB
Release : 1979
Category : Mathematics
ISBN :

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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.