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

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

Statistics Theory · Submitted 11 Dec 2013

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim The Lindeberg condition of asymptotic normality, Berry-Esseen bound, Edgeworth asymptotic expansions under weakened conditions and Cramer type large deviation results are derived.

how it is stated · asserted 1.00 read the record →

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arXiv ID1312.3256 (version 1)
Pith ID6VFUT2MI, Pith's permanent record of this paper and its review
CitationIbrahim Bin Mohamed (University of Malaya, Malaysia), Sherzod M. Mirakhmedov (Institute of Mathematics, Tashkent). "Approximation by normal distribution for a sample sum in sampling without replacement from a finite population." arXiv:1312.3256 (2013). https://pith.science/paper/6VFUT2MI
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The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

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Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 2,899 input tokens, $0.0001 reported.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.12 · human participants 0.03 · controlled comparison 0.01 · randomized assignment 0.10 · states quantitative result 0.41 · compares with prior results 0.12 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; .

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.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 A sum of observations derived by a simple random sampling design from a population of independent random variables is studied. background 0.76 0.45 0.04 asserted 0.71
s1 A procedure finding a general term of Edgeworth asymptotic expansion is presented. method 0.80 0.90 0.08 asserted 1.00
s2 The Lindeberg condition of asymptotic normality, Berry-Esseen bound, Edgeworth asymptotic expansions under weakened conditions and Cramer type large deviation results are derived. result 0.87 0.90 0.66 asserted 1.00

What kind of paper the classifier reports this is: theoretical result 0.99 · evidence from proof or derivation 1.00.

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Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper
Original 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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