## Electronic Journal of Statistics

### Size constrained unequal probability sampling with a non-integer sum of inclusion probabilities

#### Abstract

More than 50 methods have been developed to draw unequal probability samples with fixed sample size. All these methods require the sum of the inclusion probabilities to be an integer number. There are cases, however, where the sum of desired inclusion probabilities is not an integer. Then, classical algorithms for drawing samples cannot be directly applied. We present two methods to overcome the problem of sample selection with unequal inclusion probabilities when their sum is not an integer and the sample size cannot be fixed. The first one consists in splitting the inclusion probability vector. The second method is based on extending the population with a phantom unit. For both methods the sample size is almost fixed, and equal to the integer part of the sum of the inclusion probabilities or this integer plus one.

#### Article information

Source
Electron. J. Statist., Volume 6 (2012), 1477-1489.

Dates
First available in Project Euclid: 31 August 2012

https://projecteuclid.org/euclid.ejs/1346421601

Digital Object Identifier
doi:10.1214/12-EJS719

Mathematical Reviews number (MathSciNet)
MR2988455

Zentralblatt MATH identifier
1295.62010

Subjects
Primary: 62D05: Sampling theory, sample surveys

#### Citation

Grafström, Anton; Qualité, Lionel; Tillé, Yves; Matei, Alina. Size constrained unequal probability sampling with a non-integer sum of inclusion probabilities. Electron. J. Statist. 6 (2012), 1477--1489. doi:10.1214/12-EJS719. https://projecteuclid.org/euclid.ejs/1346421601

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