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

Ibrahim Bin Mohamed (University of Malaya; Malaysia); Sherzod M. Mirakhmedov (Institute of Mathematics; Tashkent)

arxiv: 1312.3256 · v1 · pith:6VFUT2MInew · submitted 2013-12-11 · 🧮 math.ST · stat.TH

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

Ibrahim Bin Mohamed (University of Malaya , Malaysia) , Sherzod M. Mirakhmedov (Institute of Mathematics , Tashkent) This is my paper

classification 🧮 math.ST stat.TH

keywords asymptoticderivededgeworthpopulationrandomsamplingapproximationberry-esseen

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

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