On the Stratification of Highly Skewed Populations (No. 1998:3). R&D Report.

This paper considers the combined problem of allocation and stratification in order to minimise the variance of the expansion estimator of a total, taking into account that the population is finite. The proof of necessary minimum variance conditions utilises the Kuhn-Tucker Theorem. Stratified simple random sampling with non-negligible sampling fractions is an important design in sample surveys. We go beyond limiting assumptions that have often been used in the past, such as that the stratification equals the study variable or that the sampling fractions are small. We discuss what difference the sampling fractions will make for stratification. In particular, in many surveys the sampling fraction equals one for some strata. The main theorem of this article is applied to a business population