A note on the sampling distribution of the information content of the priority vector of a consistent pairwise comparison judgment matrix of AHP

The sampling distribution of the information content (entropy) of the priority vector of a consistent pairwise comparison judgment matrix, PCJM(n) using the Analytic Hierarchy Process (AHP) is studied by Noble and Sanchez, where n is the number of criteria associated with the matrix. They concluded simulation experiments with sample size of 1000 and found that the distribution is normal for n=4,5,...,15. When we increased the sample size to 2000, to 3000,..., to 8000, we found that the sampling distribution of entropy is not normal for all n, n=4,5,...,15. By using BestFit software system and using sample sizes of 8000, we found that the best-fitted and the second-best-fitted distributions of the entropy are either Weibull or normal for n?4. If we consider the most number of best fitted distributions as the criteria, then Weibull should be considered as the sampling distribution of the entropy for n?4. For n=3, beta should be considered as the best-fitted distribution.