A Note on the Misuse of the Variance Test in Meteorological Studies
  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. 
Arnab Hazra, Sourabh Bhattacharya, Sabyasachi Bhattacharya, Pabitra   Banik
stat.AP stat.ME