Approximation by normal distribution for a sample sum in sampling without replacement from a finite population

Ibrahim Bin Mohamed; Sherzod M. Mirakhmedov

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arXiv · 1312.3256

Approximation by normal distribution for a sample sum in sampling without replacement from a finite population

Ibrahim Bin Mohamed·Sherzod M. Mirakhmedov

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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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Ibrahim Bin Mohamed, Sherzod M. Mirakhmedov. 2013-12-11. Approximation by normal distribution for a sample sum in sampling without replacement from a finite population. https://arxiv.org/abs/1312.3256

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