## The Annals of Statistics

### Two Conditional Limit Theorems with Applications

Lars Holst

#### 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

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