Estimation of Parameters and the Goodness-of-Fit Test for Multivariate Distributions for Data Presented as One-Dimensional Histograms

摘要

The problem of estimating parameters of multiwire probability distributions and testing hypothesis in the framework of physical experiments where data are presented as one-dimensional histograms for every single variable separately are studied. A commonly used method of some of chi/sup 2/-statistics over all single variables is investigated. It is shown that this method is incorrect for dependent variables. A correct generalization of this method is proposed for which analogues of classical theorems concerning asymptotic distributions of chi/sup 2/-statistics are proved for testing hypothesis and estimating parameters. The proposed method is implemented as a FORTRAN-4 program and illustrated by a numerical example for some model of pion-nucleon interactions. 3 refs.; 1 tab. (Atomindex citation 19:073545)