Infinite Size-Biased Orders
Abstract
Abstract The infinite random size-biased order with arbitrary positive size parameters is introduced and represented in terms of independent exponential random variables. We collect basic properties and constructions of the order, some of which belong to the folklore and some are new. Our central result shows how the isomorphism type of the order (e.g. $${\mathbb {Z}}_{>0}, {\mathbb {Q}}$$ Z > 0 , Q or any other possible) depends on the parameters. In most cases, for a given set of parameters the type is the same almost surely.
Fields of Study & Subjects
Bayesian Methods and Mixture Models
Publication details
- Journal / source
- Order
- Publisher
- Springer Science and Business Media LLC
- Volume
- 43
- Issue
- 3
- Publication date
- 25 August 2026
- Language
- EN