Study of the Quality of Several Asymptotic and Near-Exact Approximations Based on Moments for the Distribution of the Wilks Lambda and Related Statistics
by
Rui Pesado Alberto
Bela Vista High School - Setubal - Portugal
Coauthors: Carlos A. Coelho - Institute of Agriculture Technology - Portugal

A measure of proximity of distributions, when moments are known, is proposed. The measure is applied to compare approximations (asymptotic and near-exact) to distributions, mainly in situations where although being known the exact moments the exact distribution is not known. Based on cases where the exact distribution is known, some evidence is given that the proposed measure is accurate to evaluate the proximity of quantiles (exact vs. approximated). This measure is also applied to the study of several cases of telescopic near-exact approximations to the exact distribution of the Wilks Lambda statistic based on mixtures of Generalized Near-Integer Gamma distributions. Situations where the proposed measure is adequate and others where it is not are presented.

Date received: July 14, 2003