Abstract
In the important case of a symmetric distribution, it is shown that the familiar approximation leading to the normal law is actually an estimate from above. A more elementary inequality is presented first; this is much easier to prove than the final result, but it leads, nevertheless, to the solution of a nontrivial maximizing problem.
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References
A. Erdélyi, W. Magnus, F. Oberhettinger, and F. G. Tricomi, Higher transcendental functions, McGraw-Hill, N.Y., 1953, Vol. 1, p. 22.
G. G. Lorentz, Bernstein polynomials, University of Toronto Press, 1953, pp. 15, 18.
Ivan Sokolnikoff and R. M. Redheffer, Mathematics of physics and modern engineering, McGraw-Hill, N.Y., 1966, p. 624.
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© 1978 Springer Basel AG
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Ostrowski, A.M., Redheffer, R.M. (1978). Inequalities Related to the Normal Law. In: Beckenbach, E.F. (eds) General Inequalities 1 / Allgemeine Ungleichungen 1. International Series of Numerical Mathematics / Internationale Schriftenreihe zur Numerischen Mathematik / Série Internationale d’Analyse Numérique, vol 41. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-5563-1_11
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DOI: https://doi.org/10.1007/978-3-0348-5563-1_11
Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-0348-5565-5
Online ISBN: 978-3-0348-5563-1
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