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- W2435552434 abstract "The Kolmogorov distances between a symmetric hypergeometric law with standard deviation <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=sigma> <mml:semantics> <mml:mi>σ<!-- σ --></mml:mi> <mml:annotation encoding=application/x-tex>sigma</mml:annotation> </mml:semantics> </mml:math> </inline-formula> and its usual normal approximations are computed and shown to be less than <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=1 slash left-parenthesis StartRoot 8 pi EndRoot sigma right-parenthesis> <mml:semantics> <mml:mrow> <mml:mn>1</mml:mn> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mo>/</mml:mo> </mml:mrow> <mml:mo stretchy=false>(</mml:mo> <mml:msqrt> <mml:mn>8</mml:mn> <mml:mi>π<!-- π --></mml:mi> </mml:msqrt> <mml:mspace width=thinmathspace /> <mml:mi>σ<!-- σ --></mml:mi> <mml:mo stretchy=false>)</mml:mo> </mml:mrow> <mml:annotation encoding=application/x-tex>1/(sqrt {8pi },sigma )</mml:annotation> </mml:semantics> </mml:math> </inline-formula>, with the order <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=1 slash sigma> <mml:semantics> <mml:mrow> <mml:mn>1</mml:mn> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mo>/</mml:mo> </mml:mrow> <mml:mi>σ<!-- σ --></mml:mi> </mml:mrow> <mml:annotation encoding=application/x-tex>1/sigma</mml:annotation> </mml:semantics> </mml:math> </inline-formula> and the constant <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=1 slash StartRoot 8 pi EndRoot> <mml:semantics> <mml:mrow> <mml:mn>1</mml:mn> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mo>/</mml:mo> </mml:mrow> <mml:msqrt> <mml:mn>8</mml:mn> <mml:mi>π<!-- π --></mml:mi> </mml:msqrt> </mml:mrow> <mml:annotation encoding=application/x-tex>1/sqrt {8pi }</mml:annotation> </mml:semantics> </mml:math> </inline-formula> being optimal. The results of Hipp and Mattner (2007) for symmetric binomial laws are obtained as special cases. Connections to Berry-Esseen type results in more general situations concerning sums of simple random samples or Bernoulli convolutions are explained. Auxiliary results of independent interest include rather sharp normal distribution function inequalities, a simple identifiability result for hypergeometric laws, and some remarks related to Lévy’s concentration-variance inequality." @default.
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- W2435552434 date "2017-09-07" @default.
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- W2435552434 title "On normal approximations to symmetric hypergeometric laws" @default.
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- W2435552434 doi "https://doi.org/10.1090/tran/6986" @default.
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