A Characterization of GEM Distributions
- 1 May 2001
- journal article
- research article
- Published by Cambridge University Press (CUP) in Combinatorics, Probability and Computing
- Vol. 10 (3) , 213-217
- https://doi.org/10.1017/s0963548301004692
Abstract
Let (Xn) be a residual allocation model with i.i.d. residual fractions Un: For W a random variable with values in [0; 1] and independent of (Xn), we define another sequence (Yn) by setting(formula here)Under minor regularity assumptions we show that (Xn) and (Yn) have the same probability law if and only if this law is a GEM distribution. In this case, the distribution of W and the Uns is Beta(1; θ) for some θ > 0.Keywords
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