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

Abstract

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.

Keywords:

• analytic hierarchy process
• consistent matrix
• priority vector
• information content
• entropy
• sampling distribution of entropy