Abstract
Assume that there is a random number K of positive integer random variables S1, …, SK that are conditionally independent given K and all have identical distributions. A random integer partition N = S1 + S2 + … + SK arises, and we denote by PN the conditional distribution of this partition for a fixed value of N. We prove that the distributions {PN}N=1∞ form a partition structure in the sense of Kingman if and only if they are governed by the Ewens-Pitman Formula. The latter generalizes the celebrated Ewens sampling formula, which has numerous applications in pure and applied mathematics. The distributions of the random variables K and Sj belong to a family of integer distributions with two real parameters, which we call quasi-binomial. Hence every Ewens-Pitman distribution arises as a result of a two-stage random procedure based on this simple class of integer distributions. Bibliography: 25 titles.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
