A note on the sampling distribution of the information content of the priority vector of a consistent pairwise comparison judgement matrix of analytic hierarchy process

A note on the sampling distribution of the information content of the priority vector of a consistent pairwise comparison judgement matrix of analytic hierarchy process

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Article ID: iaor2001927
Country: United Kingdom
Volume: 51
Issue: 2
Start Page Number: 237
End Page Number: 240
Publication Date: Feb 2000
Journal: Journal of the Operational Research Society
Authors: ,
Keywords: analytic hierarchy process
Abstract:

The sampling distribution of the information content (entropy) of the priority vector of a consistent pairwise comparison judgement matrix, PCJM(n) using the Analytic Hierarchy Process 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.

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