Generalized Pearson Distributions and Nonlinear Programing

A generalization of the Pearson curves is obtained as the solution to the differential equation which best fits a histogram in the mean square and satisfies certain statistical constraints, e.g., the mean and variance may be prescribed. Φ is the theoretical distribution defined on the intervel is a rational function with numerator and denomenator orders of mand n, respevtively. The values of the coefficients in are obtained from a Powell minimization of the mean-square value plus sum-of-squares constraints. Excellent fits are obtained effciently which, furthermore, are capable of providing an analytical representation of an infinite tail. An accurate initial approximation of for starting the Powell minimization is obtained from a symbol manipulation code in PL/1—Formac and based on the visual decomposition of a histogram into sums of normal curves.