On computing the number of distinct values occurring in generalized Dirichlet process samples

Abstract This paper studies the generalized Dirichlet process ( \(GDP\) ) with its main properties, including moments of random weights and tail moments. We present the truncated \(GDP\ as a finite mixture distribution and assess the error bounds caused by the truncation. This tactic provides more practicable stick-breaking priors in nonparametric Bayesian settings and facilitates computation. We obtain the joint density of random weights, show that the number of distinct values varies on raising the GDP samples, and present the impact of the precision parameter on this number. We also show that our results coincide with the Dirichlet process \((DP)\) . MSC Classification: 62E15 , 60C05 , 97K60