Some Limit Theorems for the Indistinguishable Ball Problem with Applications in Nonparametrics.
Abstract
Consider the following urn model, m urns and distribute n indistinguishable balls among the urns such that the distinguishable distributions of the balls all have the same probability. Let S sub K denote the number of balls in the Kth urn. Clearly S sub 1 + ... + S sub m = n. In this paper, random variables of the type Z = h(S sub 1,...,S sub m), especially h(S sub 1, ...,S sub m) = h sub 1 (S sub 1) + ... + h sub m (S sub m), are studied when m,n approaches the limit of infinity m/n approaches the limit of rho, o < rho < infinity. Some applications of the results in nonparametric statistics are briefly discussed and the limit distribution of mas(S sub1,...,S sub m) is derived.
Document Details
- Document Type
- Technical Report
- Publication Date
- Aug 01, 1976
- Accession Number
- ADA031957
Entities
People
- Lars Holst
Organizations
- University of Wisconsin–Madison