TITLE:
Sampling Designs with Linear and Quadratic Probability Functions
AUTHORS:
Lennart Bondesson, Anton Grafström, Imbi Traat
KEYWORDS:
Complementary Midzuno Design; Conditional Sample; Inclusion Probability; Midzuno Design; Mixture of Designs; Parameters of Design; Sample Complement; Sinha Design
JOURNAL NAME:
Open Journal of Statistics,
Vol.4 No.3,
March
28,
2014
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.