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 prior ity Vector of a consistent pairwise comparison judgment matrix, PCJM(n) usi ng the Analytic Hierarchy Process (AHP) is studied by Noble and Sanchez, wh ere n is the number of criteria associated with the matrix. They concluded simulation experiments with sample size of 1000 and found that the distribu tion is normal for n = 4, 5,..., 15. When we increased the sample size to 2 000, to 3000,..., to 8000, we found that the sampling distribution of entro py is not normal for all n, n = 4, 5,..., 15. By using BestFit software sys tem and using sample sizes of 8000, we found that the best-fitted and the s econd-best-fitted distributions of the entropy are either Weibull or normal for n greater than or equal to 4. if we consider the most number of best f itted distributions as the criteria, then Weibull should be considered as t he sampling distribution of the entropy for n greater than or equal to 4. F or n = 3, beta should be considered as the best-fitted distribution.