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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

Author

Listed:
  • V M Rao Tummala

    (Eastern Michigan University)

  • H Ling

    (Fudan University)

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.

Suggested Citation

  • V M Rao Tummala & H Ling, 2000. "A note on the sampling distribution of the information content of the priority vector of a consistent pairwise comparison judgment matrix of AHP," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 51(2), pages 237-240, February.
  • Handle: RePEc:pal:jorsoc:v:51:y:2000:i:2:d:10.1057_palgrave.jors.2600857
    DOI: 10.1057/palgrave.jors.2600857
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    Cited by:

    1. Beynon, Malcolm, 2002. "An analysis of distributions of priority values from alternative comparison scales within AHP," European Journal of Operational Research, Elsevier, vol. 140(1), pages 104-117, July.

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