On Families of Distributions for Which Optimal Bounds on Expectations of GOS Can be Derived

DOI10.1080/03610920701832466zbMath1144.62034OpenAlexW2138475802MaRDI QIDQ3526057

Mariusz Bieniek

Publication date: 24 September 2008

Published in: Communications in Statistics - Theory and Methods (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/03610920701832466

zbMATH Keywords

projection methodgeneralized order statisticsgeneralized Pareto distributionsharp boundgeneralized failure rate

Mathematics Subject Classification ID

Inequalities; stochastic orderings (60E15) Order statistics; empirical distribution functions (62G30) Reliability and life testing (62N05)

Related Items (14)

Quantile Inequalities for the Expectations of GeneralizedL-Statistics ⋮ Sharp bounds for the mean of the total time on test for distributions with increasing generalized failure rate ⋮ Preservation of distributional properties of component lifetimes by system lifetimes ⋮ Optimal bounds for the mean of the total time on test for distributions with decreasing generalized failure rate ⋮ Relations for \(m\)-generalized order statistics via an Opial-type inequality ⋮ Evaluations of generalized order statistics from bounded populations ⋮ Optimal bounds on expectations of order statistics and spacings from nonparametric families of distributions generated by convex transform order ⋮ On unimodality of the lifetime distribution of coherent systems with failure-dependent component lifetimes ⋮ Optimal upper bounds on expected kth record values from IGFR distributions ⋮ Non-positive upper bounds on expectations of low rank order statistics from DFR populations ⋮ Sharp lower bounds on expectations of gOS based on DGFR distributions ⋮ Bounds on the expectations of \(L\)-statistics based on iid life distributions ⋮ Optimal evaluations for the bias of trimmed means of \(k\)th record values ⋮ Maximal Expectations of Extreme Order Statistics from Increasing Density and Failure Rate Populations

Cites Work

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• Variation diminishing property of densities of uniform generalized order statistics
• Contributions to nonparametric generalized failure rate function estimation
• Statistical inference using extreme order statistics
• Projection method for moment bounds on order statistics from restricted families. II: Independent case
• Marginal distributions of sequential and generalized order statistics
• Unimodality of uniform generalized order statistics, with applications to mean bounds
• A concept of generalized order statistics
• Projection method for moment bounds on order statistics from restricted families
• Projection bounds on expectations of generalized order statistics from DD and DDA families
• Projection bounds on expectations of generalized order statistics from DFR and DFRA families
• Projection Mean–Variance Bounds on Expectations ofkth Record Values from Restricted Families
• Sharp upper mean-variance bounds for trimmed means from restricted families
• Optimal mean-variance bounds on order statistics from families determined by star ordering
• Projecting statistical functionals

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