On a class of non-regenerative sampling distributions. (English) Zbl 1125.62122

Möhle, Martin

Comb. Probab. Comput. 16, No. 3, 435-444 (2007).

Summary: We show that the sampling formula induced from a \(\Lambda\)-coalescent process with multiple collisions is regenerative if and only if the measure \(\Lambda\) is either concentrated in 0 (Kingman case) or concentrated in 1 (star-shaped case). The Ewens sampling formula is the only sampling formula in this class which also belongs to Pitman’s two-parameter family of sampling distributions.

MSC:

62P10	Applications of statistics to biology and medical sciences; meta analysis
92D10	Genetics and epigenetics