Resumen de The Hypergeometric Sampling Design, Theory and Practice

Imbi Traat, Maiki Ilves

• The main aim of this paper is to point out that a classical hypergeometric distribution can be viewed as an exact probabilistic description of a selection mechanism in many practical sample surveys. This selection mechanism, the hypergeometric (HG) sampling design, is an unequal probability with-replacement design. Exploiting properties of the HG distribution many useful results can be derived for sample surveys. In this paper we give the estimation formulae under the HG design. We also derive the inclusion probabilities of a related design, received by neglecting repeated elements from a HG sample. We show that a HG design coupled with a HG design in the second phase results in a two-phase design which is again HG. This property is used when deriving a Jackknife variance formula for a linear estimator under the HG design. Finally we consider the equal probability designs received from the HG design by a suitable sub-sampling procedure in the second phase. We give estimation formulae for some of such designs.