A Characterization of GEM Distributions

Source abstract

Let ( X n ) be a residual allocation model with i.i.d. residual fractions U n : For W a random variable with values in [0; 1] and independent of ( X n ), we define another sequence ( Y n ) by setting (formula here) Under minor regularity assumptions we show that ( X n ) and ( Y n ) have the same probability law if and only if this law is a GEM distribution. In this case, the distribution of W and the U n s is Beta(1; θ) for some θ > 0.