CURVE FITTING PROBABILITY DENSITY FUNCTIONS USING THE H-FUNCTION (STATISTICS)

A numerical solution for determining the Maximum Likelihood estimates for the parameters of an H-function distribution is presented. A solution for estimating the parameters given only values of moments of the sample data by use of a "method of moments" technique is also discussed. The H-function distribution determines a set of families of probability distributions. The class of first-order distributions includes many of the classical probability distributions including the exponential, Gamma, Chi-Square, Maxwell, Half-normal, Rayleigh, and Weibull distributions. By using the techniques presented in this dissertation one can fit a distribution to a data set with better fit than would be possible using one of the afore mentioned distributions.;Background material is presented on both the H-function and the H-function distribution as well as the important aspects of estimation theory. Numerical techniques for finding roots to an equation and for maximizing the value of the likelihood function are also given. A simplified solution for solving the first-order parameters using the "method of moments" is given. Numerical examples for fitting random samples drawn from classical distributions previously mentioned are given.;The correspondence between the first-order H-function family and the Generalized Gamma distribution is shown. This correspondence is used to reduce the maximum likelihood solution solution from one involving three unknowns to one with only a single unknown.;A geometric representation of distributions as points in the parameter space for the H-function is given with geometric interpretation of special movements in that space. Uniqueness of representation of the parameters in a subset of this space is also shown.