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Unimodality of uniform generalized order statistics,with applications to mean bounds |
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| Authors: | Cramer Erhard Kamps Udo Rychlik Tomasz |
| Affiliation: | (1) Institute of Mathematics, University of Oldenburg, PO Box 2503, D-26111 Oldenburg, Germany;(2) Institute of Mathematics, Polish Academy of Sciences, Chopina 12, 87100 Toruń, Poland |
| Abstract: | We prove that uniform generalized order statistics are unimodal for an arbitrary choice of model parameters. The result is applied to establish optimal lower and upper bounds on the expectations of generalized order statistics based on nonnegative samples in the population mean unit of measurement. The bounds are attained by two-point distributions. |
| Keywords: | Generalized order statistics uniform sample nonnegative sample unimodal distribution expectation optimal bound |
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