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Keywords:

  • complementary sampling;
  • conditional Poisson sampling;
  • CP(2) sampling;
  • entropy;
  • Gibbs sampling;
  • inclusion probabilities;
  • linear programming;
  • Pareto sampling;
  • Sampford sampling;
  • Sinha's method

Abstract.  Methods to perform fixed size sampling with prescribed second-order inclusion probabilities are presented. The focus is on a conditional Poisson design of order 2, a CP(2) design. It is an exponential design of quadratic type and it is carefully studied. In particular, methods to find the suitable values of the parameters and methods to sample are described. Small examples illustrate.