The Chinese restaurant process with parameter α 0 generates a random partition of a set of integers { 1,2,. . . , n}. Each random partition generated by the Chinese restaurant process consists of n(p) disjoint subsets of the integers. It is known that n(p) ~ α log_e(n) when n is large, see Korwar and Hollander [1]....[ Read more ]

The Chinese restaurant process with parameter α > 0 generates a random partition of a set of integers { 1,2,. . . , n}. Each random partition generated by the Chinese restaurant process consists of n(p) disjoint subsets of the integers. It is known that n(p) ~ α log_e(n) when n is large, see Korwar and Hollander [1].

The weighted Chinese restaurant process generalizes the Chinese restaurant process by allocating the integers according to an additional weighting scheme. The weighted Chinese restaurant process also produces n(p) disjoint subsets of the set of integers. The distribution of the random variable n(p) for the weighted Chinese restaurant process is discussed in this thesis using numerical examples. We also show that when the weights are bounded, the random variable n(p) will increase to infinity with probability one when n increases to infinity. Furthermore, numerical work seems to suggest that the growth rate of the n(p) is also O(log_e(n)).