Sharp bounds on the expectations of second record values from symmetric populations |
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Authors: | Mohammad Z Raqab Tomasz Rychlik† |
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Institution: | 1. University of Jordan, Department of Mathematics , Amman, Jordan , 11942mraqab@accessme.com.jo;3. Polish Academy of Sciences, Institute of Mathematics , Chopina 12, Toruń, Poland , 87100 |
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Abstract: | 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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Keywords: | Record statistics Bounds for moments Symmetric population Hölder inequality pth central absolute moment Moriguti monotone approximation |
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