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Approximation by Normal Distribution for a Sample Sum in Sampling Without Replacement from a Finite Population

Author

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  • Ibrahim Bin Mohamed

    (University of Malaya)

  • Sherzod M. Mirakhmedov

    (Institute of Mathematics)

Abstract

A sum of observations derived by a simple random sampling design from a population of independent random variables is studied. A procedure finding a general term of Edgeworth asymptotic expansion is presented. The Lindeberg condition of asymptotic normality, Berry-Esseen bound, Edgeworth asymptotic expansions under weakened conditions and Cramer type large deviation results are derived.

Suggested Citation

  • Ibrahim Bin Mohamed & Sherzod M. Mirakhmedov, 2016. "Approximation by Normal Distribution for a Sample Sum in Sampling Without Replacement from a Finite Population," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 78(2), pages 188-220, August.
    • Handle: RePEc:spr:sankha:v:78:y:2016:i:2:d:10.1007_s13171-016-0088-9
    DOI: 10.1007/s13171-016-0088-9
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    References listed on IDEAS

    as
    1. Babu, G. Jogesh & Singh, Kesar, 1985. "Edgeworth expansions for sampling without replacement from finite populations," Journal of Multivariate Analysis, Elsevier, vol. 17(3), pages 261-278, December.
    2. Babu, Gutti Jogesh & Bai, Z. D., 1996. "Mixtures of Global and Local Edgeworth Expansions and Their Applications," Journal of Multivariate Analysis, Elsevier, vol. 59(2), pages 282-307, November.
    3. Mirakhmedov, Sherzod A., 2005. "Lower estimation of the remainder term in the CLT for a sum of the functions of k-spacings," Statistics & Probability Letters, Elsevier, vol. 73(4), pages 411-424, July.
    Full references (including those not matched with items on IDEAS)

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