A multinomial distribution describes the outcomes of independent trials with two or more possible, mutually exclusive outcomes. This approach is used to redistribute cases of disease among spatially or temporally referenced sub-groups (bins) under analysis. Cases are distributed at random among bins, where the probability of a case being placed in a particular bin is proportional to the population-at-risk size in that bin.
The figure below shows a simple example of this process. There are four bins (a, b, c, and d) that have population sizes of (10, 50, 20, and 20). The interval from 0-1 is partitioned among them, with each bin getting an interval proportional to its relative size (so 1/10, 1/2, 1/5, and 1/5 respectively). Then, as a random number generator supplies values between 0-1, each value falls into a particular bin and counts as a case in that bin.
This randomization technique is used in Besag
and Newell's, Bithell's
