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

Author(s): Ibrahim Bin Mohamed and Sherzod M. Mirakhmedov
Issue: Volume 78 Series A Part 2 Year 2016
Pages: 188 -- 220
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.
AMS (2000) subject classification . Primary: 62G20, Secondary: 60F05.
Keywords and phrases: Berry-Esseen bound, Edgeworth expansion, Lindeberg condition, Large deviation, Finite population, Sample sum, Sampling without replacement.