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.
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Mohamed, I.B., Mirakhmedov, S.M. Approximation by Normal Distribution for a Sample Sum in Sampling Without Replacement from a Finite Population. Sankhya A 78, 188–220 (2016). https://doi.org/10.1007/s13171-016-0088-9
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DOI: https://doi.org/10.1007/s13171-016-0088-9