Bounds for the expectation of the kth root of a random variable

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摘要

Exact bounds for the mean value of a fractional moment, such as the sample standard deviation, are considered. These bounds are compared with those found by summation techniques applied to computer extended series. An expansion involving an arbitrary parameter is introduced, and now best bounds are found by optimization. There are applications to bounds for a certain class of quadrature problem.

论文关键词:Asymptotic series,generalized bounds,quadrature formulas,root transformations,standard deviation limits,remainders

论文评审过程:Received 24 October 1983, Available online 10 July 2002.

论文官网地址:https://doi.org/10.1016/0377-0427(84)90060-8