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Sharp bounds on the expectations of second record values from symmetric populations
Journal article   Peer reviewed

Sharp bounds on the expectations of second record values from symmetric populations

Mohammad Z. Raqab and Tomasz Rychlik†
Statistics (Berlin, DDR), Vol.38(1), pp.49-57
01/02/2004
DOI: https://doi.org/10.1080/0233188032000158808

Abstract

Bounds for moments Hölder inequality Moriguti monotone approximation pth central absolute moment Record statistics Symmetric population
Combining the greatest convex minorant approximation (Moriguti, S. (1953). A modification of Schwarz's inequality with applications to distributions. Ann. Math. Statist., 24, 107-113.) with the Hölder inequality, we establish sharp bounds on the expectations of the second record statistics from symmetric populations. We also determine the distributions for which the bounds are attained. The optimal bounds are numerically evaluated and compared with other classical rough ones.

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