A Note on the Misuse of the Variance Test in Meteorological Studies

TL;DR

This paper critiques the misuse of variance tests in meteorology, demonstrating that the assumed asymptotic distribution is often invalid and proposing a method to verify its applicability.

Contribution

It clarifies the incorrect assumptions behind variance tests in meteorological data analysis and offers a way to validate the test's asymptotic distribution.

Findings

Asymptotic distribution often not comparable to chi-square

Method to check validity of the asymptotic distribution

Highlights common misuse in meteorological variance testing

Abstract

The erroneous assumption "for all distributions for which the theoretical variance can be computed independently from parameters estimated by any method different from the method of moments" has been used in the case of fitting the gamma distribution to a rainfall data by Mooley (1973) which was followed by several researchers. We show that the asymptotic distribution of the test statistic is generally not even comparable to any central chi-square distribution. We also describe a method for checking the validity of the asymptotic distribution for a class of distributions.