Sampling design and sample selection through distribution theory

This paper may be seen as in part a review covering basics of sampling theory in a different light. We use a multivariate approach with a unifying treatment of WOR and WR sampling designs. In this framework, we present probability functions of several important sampling designs, such as the hypergeometric, the conditional Poisson, the Sampford, and the general order sampling designs among others. Benefiting from the distributional feature of the sampling design, a list-sequential method for generating a sample from any given design is developed. The method is applied to hypergeometric, multinomial, conditional Poisson and Sampford designs. An order sampling procedure for a population with unknown size is described. Markov chain Monte Carlo methods are discussed.