Unimodality of uniform generalized order statistics, with applications to mean bounds

DOI10.1007/BF02530531zbMath1050.62058OpenAlexW1997690727MaRDI QIDQ1881012

Udo Kamps, Erhard Cramer, Tomasz Rychlik

Publication date: 27 September 2004

Published in: Annals of the Institute of Statistical Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02530531

zbMATH Keywords

expectationoptimal boundunimodal distributionuniform samplenonnegative sample

Mathematics Subject Classification ID

Inequalities; stochastic orderings (60E15) Order statistics; empirical distribution functions (62G30) Characterization and structure theory of statistical distributions (62E10)

Related Items (30)

Progressive censoring methodology: an appraisal (with comments and rejoinder) ⋮ Comparisons of the expectations of system and component lifetimes in the failure dependent proportional hazard model ⋮ Some new results on likelihood ratio ordering and aging properties of generalized order statistics ⋮ Distances between models of generalized order statistics ⋮ Discrete strong unimodality of order statistics ⋮ Likelihood ratio comparisons and logconvexity properties ofp-spacings from generalized order statistics ⋮ HR and RHR orderings of generalized order statistics ⋮ Relations for \(m\)-generalized order statistics via an Opial-type inequality ⋮ On Families of Distributions for Which Optimal Bounds on Expectations of GOS Can be Derived ⋮ Some new results on unimodality of generalized order statistics and their spacings ⋮ Evaluations of generalized order statistics from bounded populations ⋮ STOCHASTIC COMPARISONS OF SYSTEMS BASED ON SEQUENTIAL ORDER STATISTICS VIA PROPERTIES OF DISTORTED DISTRIBUTIONS ⋮ Projection bounds on expectations of generalized order statistics from DD and DDA families ⋮ Dynamic Signatures of Coherent Systems Based on Sequential Order Statistics ⋮ Logconcavity and unimodality of progressively censored order statistics ⋮ Projection Bounds on Expectations of Spacings of Generalized Order Statistics from DD and DDA Families ⋮ Evaluating expectations of \(L\)-statistics by the Steffensen inequality ⋮ On unimodality of the lifetime distribution of coherent systems with failure-dependent component lifetimes ⋮ A NOTE ON CHARACTERIZATIONS OF DISTRIBUTIONS BY REGRESSIONS OF NON-ADJACENT GENERALIZED ORDER STATISTICS ⋮ Type-I censored sequential \(k\)-out-of-\(n\) systems ⋮ Variation diminishing property of densities of uniform generalized order statistics ⋮ On characterizations of distributions by regression of adjacent generalized order statistics ⋮ Projection bounds on expectations of spacings of generalized order statistics from DFR and DFRA families ⋮ Marginal Distributions of the Counting Process Associated with Generalized Order Statistics ⋮ Projection bounds on expectations of generalized order statistics from DFR and DFRA families ⋮ Sharp lower bounds on expectations of gOS based on DGFR distributions ⋮ Optimal equivariant prediction regions based on multiply type-II censored generalized order statistics from exponential distributions ⋮ Fisher information in generalized order statistics ⋮ SOME CONVEXITY PROPERTIES OF THE DISTRIBUTION OF LOWER k-RECORD VALUES WITH EXTENSIONS ⋮ On the existence of moments of generalized order statistics.

Cites Work

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• On characterizations of distributions via moments of record values
• Bounds based on greatest convex minorants for moments of record values
• Exact bounds for the expectations of order statistics from non-negative populations
• Marginal distributions of sequential and generalized order statistics
• On the Moments of the Sample Quantiles
• ON THE EXPECTED VALUES OF RECORD VALUES¹
• Sharp bounds on l-estimates and their expectations for dependent samples
• Evaluations of expected generalized order statistics in various scale units
• A Modification of Schwarz's Inequality with Applications to Distributions
• Projecting statistical functionals
• Bounds for means and variances of progressive type II censored order statistics

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