Sampling Designs with Linear and Quadratic Probability Functions

Lennart Bondesson, Anton Grafström, Imbi Traat

Department of Forest Resource Management, Swedish University of Agricultural Sciences, Ume?, Sweden.
Department of Mathematics and Mathematical Statistics, Ume? University, Ume?, Sweden.
Institute of Mathematical Statistics, University of Tartu, Tartu, Estonia.

DOI: 10.4236/ojs.2014.43017                

Abstract

Fixed size without replacement sampling designs with probability functions that are linear or quadratic functions of the sampling indicators are defined and studied. Generality, simplicity, remarkable properties, and also somewhat restricted flexibility characterize these designs. It is shown that the families of linear and quadratic designs are closed with respect to sample complements and with respect to conditioning on sampling outcomes for specific units. Relations between inclusion probabilities and parameters of the probability functions are derived and sampling procedures are given.

Keywords

Complementary Midzuno Design; Conditional Sample; Inclusion Probability; Midzuno Design; Mixture of Designs; Parameters of Design; Sample Complement; Sinha Design

Conflicts of Interest

The authors declare no conflicts of interest.

References

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