**Sankhya:
The Indian Journal of Statistics**

2003, Volume 65, Pt. 2, 389--410

**A Central Limit Theorem For The
Mean In Rejective Sampling**

By

PHILIPPE BARBE, Centre National de la Recherche Scientifique, Paris, France

SUMMARY: We prove a central limit theorem for the empirical mean of a rejective sample of size $n$ in a population of size $N$ as $N$ tends to infinity. Among other things, we assume that the population consists of a finite number of subpopulations and that the probability for a given unit to be sampled depends only on its belonging to a subpopulation. In the course of proving the main result, we also obtain a central limit for the generalized hypergeometric distribution which is of independent interest.

*AMS (1991) subject classification. *60F05, 62E20.

*Key words and phrases. *Rejective sample, conditional central limit
theorem, extended hypergeometric distribution, linear rank statistics,
heterogeneity.