## The Annals of Statistics

- Ann. Statist.
- Volume 7, Number 3 (1979), 551-557.

### Two Conditional Limit Theorems with Applications

#### Abstract

Let $(X_1, Y_1),\cdots, (X_N, Y_N)$ be i.i.d. rv's where the $X$'s are nonnegative integer-valued. Conditional on $\sigma X_k$ the asymptotic distribution of $\sigma Y_k$ and $\sigma a_k X_k$ are derived by general methods. Some applications are briefly discussed: sampling without replacement, the classical occupancy problem, the Wilcoxon statistic, the Poisson index of dispersion, testing geometric versus Poisson distribution.

#### Article information

**Source**

Ann. Statist., Volume 7, Number 3 (1979), 551-557.

**Dates**

First available in Project Euclid: 12 April 2007

**Permanent link to this document**

https://projecteuclid.org/euclid.aos/1176344676

**Digital Object Identifier**

doi:10.1214/aos/1176344676

**Mathematical Reviews number (MathSciNet)**

MR527490

**Zentralblatt MATH identifier**

0406.62008

**JSTOR**

links.jstor.org

**Subjects**

Primary: 62E20: Asymptotic distribution theory

Secondary: 60F05: Central limit and other weak theorems

**Keywords**

Limit theorems occupancy problems sampling without replacement testing fit of Poisson distribution conditioning with sufficient statistics nonparametrics urn models

#### Citation

Holst, Lars. Two Conditional Limit Theorems with Applications. Ann. Statist. 7 (1979), no. 3, 551--557. doi:10.1214/aos/1176344676. https://projecteuclid.org/euclid.aos/1176344676