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A Note on the Sampling Distribution of the Information Content of the Priority Vector of a Consistent Pairwise Comparison Judgment Matrix of AHP
V. M. Rao Tummala and H. Ling
The Journal of the Operational Research Society
Vol. 51, No. 2 (Feb., 2000), pp. 237-240
Stable URL: http://www.jstor.org/stable/254264
Page Count: 4
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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.
The Journal of the Operational Research Society © 2000 Operational Research Society