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Algorithms to Find Exact Inclusion Probabilities for Conditional Poisson Sampling and Pareto πps Sampling Designs

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  • Nibia Aires

    (Chalmers University of Technology)

Abstract

Conditional Poisson Sampling Design as developed by Haje´k may be defined as a Poisson sampling conditioned by the requirement that the sample has fixed size. In this paper, an algorithm is implemented to calculate the conditional inclusion probabilities given the inclusion probabilities under Poisson Sampling. A simple algorithm is also given for second order inclusion probabilities in Conditional Poisson Sampling. Furthermore a numerical method is introduced to compute the unconditional inclusion probabilities when the conditional inclusion probabilities are predetermined. Simultaneously, we study the Pareto πps sampling design. This method, introduced by Rose´n, belongs to a class of sampling schemes called Order Sampling with Fixed Distribution Shape. Methods are provided to compute the first and second order inclusion probabilities numerically also in this case, as well as two procedures to adjust the parameters to get predetermined inclusion probabilities.

Suggested Citation

  • Nibia Aires, 1999. "Algorithms to Find Exact Inclusion Probabilities for Conditional Poisson Sampling and Pareto πps Sampling Designs," Methodology and Computing in Applied Probability, Springer, vol. 1(4), pages 457-469, December.
    • Handle: RePEc:spr:metcap:v:1:y:1999:i:4:d:10.1023_a:1010091628740
    DOI: 10.1023/A:1010091628740
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    Cited by:

    1. Zoran Utkovski & Melanie F Pradier & Viktor Stojkoski & Fernando Perez-Cruz & Ljupco Kocarev, 2018. "Economic complexity unfolded: Interpretable model for the productive structure of economies," PLOS ONE, Public Library of Science, vol. 13(8), pages 1-24, August.
    2. Carrizosa, Emilio, 2010. "Unequal probability sampling from a finite population: A multicriteria approach," European Journal of Operational Research, Elsevier, vol. 201(2), pages 500-504, March.
    3. Matei, Alina & Tille, Yves, 2007. "Computational aspects of order [pi]ps sampling schemes," Computational Statistics & Data Analysis, Elsevier, vol. 51(8), pages 3703-3717, May.
    4. Lennart Bondesson, 2010. "Conditional and Restricted Pareto Sampling: Two New Methods for Unequal Probability Sampling," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 37(3), pages 514-530, September.

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