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Several extensions of the familiar Dirichlet process have been widely investigated to nonparametric Bayesian model fittings parallel with appealing subsequent studies on their particular properties. This paper presents an explicit form for the joint distribution of drawn samples from the beta two-parameter process using an extension of stick-breaking construction. In particular, we evaluate the joint distribution of a random sequence for a specific process case and compare it with the Blackwell-MacQueen process. We obtain moments of the beta two-parameter process and present a formula for the number of distinct values in the sample. We establish the precision ratio and explore its effect on this number.
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