AMERICAN JOURNAL OF MATHEMATICAL AND MANAGEMENT SCIENCES Copyright© 1987 by American Sciences Press, Inc. APPLICATIONS OF THE H-FUNCTION DISTRIBUTION IN CLASSIFYING AND FITTING CLASSICAL PROBABILITY DISTRIBUTIONS Henry Jacobs Texas Instruments Incorporated Austin, Texas 78769 J. Wesley Barnes The University of Texas at Austin Austin, Texas 78712 Ivy D. Cook, Jr. Air Force Institute of Technology Wright-Patterson Air Force Base, Ohio 45433 SYNOPTIC ABSTRACT The H-function is a general mathematical function which includes families of statistical distributions; these include most classical univariate statistical distributions. A representation of these classical distributions as points in the parameter space of the H-function parameters is developed, together with a geometric representation of some common algebraic operations on random variables. Techniques for estimation of the H-function parameters using the "method of moments" are also given. Key Words and Phrases: statistical analysis; probability distributions; probability density functions; special functions; H-function; parameter estimation; curve-fitting; method of moments. 1987, VOL. 7, NOS. 1 & 2, 131-147 0196-6324/87/010131-17 $6.40 131