Sampling formulae arising from random Dirichlet populations. (English) Zbl 1065.60050
Summary: Consider the random Dirichlet partition of the interval into \(n\) fragments at temperature \(\theta > 0\). Some statistical features of this random discrete distribution are recalled, together with explicit results on the law of its size-biased permutation. Using these, pre-asymptotic versions of the Ewens and Donnelly-Tavaré-Griffiths sampling formulae from finite Dirichlet partitions are computed exactly. From these, new proofs of the usual sampling formulae from random proportions with GEM\((\gamma)\) distribution are supplied, when considering the Kingman limit \(n \uparrow \infty\), \(\theta \downarrow 0\) while \(n\theta =\gamma > 0\).
MSC:
| 60G57 | Random measures |
| 62E17 | Approximations to statistical distributions (nonasymptotic) |
| 60K99 | Special processes |
| 62E15 | Exact distribution theory in statistics |
| 62E20 | Asymptotic distribution theory in statistics |
Keywords:
Dirichlet partition; Ewens and Donnelly-Tavaré-Griffiths sampling formulae; gem; random discrete distribution; size-biased permutationReferences:
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