Sampling distribution of the random consistency index of the analytic hierarchy process(AHP)

Several AHP researchers have addressed the problem of computing the mean random consistency index( MRCI(n)). No one, to our knowledge, determined the sampling distribution of the random consistency index, (RCI(n)), of the pairwise comparison judgment matrix of dimension n. RCI(n) is the basis for defining the MRCI(n) and the consistency ratio, CR(n). Finding the sampling distribution of RCI(n) may enable us to determine the distribution of CR(n). In this paper we conducted extensive simulation experiments to determine the sampling distribution of RCI(n) and found that the normal distribution can be used as the best fitted distribution for n⩾ 5. For n=3 and 4 the Weibull distribution can be used as the best fitted distribution.