## The Annals of Probability

- Ann. Probab.
- Volume 5, Number 5 (1977), 814-817.

### A Generalization of the Karlin-McGregor Theorem on Coincidence Probabilities and an Application to Clustering

#### Abstract

Karlin and McGregor calculated the coincidence probabilities for $n$ particles independently executing a Markov process of a certain class. This note extends their result by allowing the particles to have different stopping times. Applied to a one-dimensional clustering problem, this gives a new solution computationally simpler than previous ones.

#### Article information

**Source**

Ann. Probab., Volume 5, Number 5 (1977), 814-817.

**Dates**

First available in Project Euclid: 19 April 2007

**Permanent link to this document**

https://projecteuclid.org/euclid.aop/1176995725

**Digital Object Identifier**

doi:10.1214/aop/1176995725

**Mathematical Reviews number (MathSciNet)**

MR471014

**Zentralblatt MATH identifier**

0375.60076

**JSTOR**

links.jstor.org

**Subjects**

Primary: 60J05: Discrete-time Markov processes on general state spaces

Secondary: 60E05: Distributions: general theory

**Keywords**

Coincidence probabilities Markov process stopping time cluster generalized birthday problem

#### Citation

Hwang, F. K. A Generalization of the Karlin-McGregor Theorem on Coincidence Probabilities and an Application to Clustering. Ann. Probab. 5 (1977), no. 5, 814--817. doi:10.1214/aop/1176995725. https://projecteuclid.org/euclid.aop/1176995725