Bounds on the expectations of \(L\)-statistics based on iid life distributions

DOI10.3103/S1066530722020041OpenAlexW4312355968MaRDI QIDQ2082289

Tomasz Rychlik

Publication date: 4 October 2022

Published in: Mathematical Methods of Statistics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3103/s1066530722020041

zbMATH Keywords

order statisticindependent identically distributed random variables\(L\)-statisticsharp boundlife distribution

Mathematics Subject Classification ID

Inequalities; stochastic orderings (60E15) Order statistics; empirical distribution functions (62G30)

Cites Work

• Evaluations of expectations of order statistics and spacings based on IFR distributions
• Improving the Hartley-David-Gumbel bound for the mean of extreme order statistics
• Bounds on expectations of small order statistics from decreasing density populations
• Sharp lower bounds on expectations of gOS based on DGFR distributions
• A simple application of binomial -- negative binomial relationship in the derivation of sharp bounds for moments of order statistics based on greatest convex minorants
• Projection method for moment bounds on order statistics from restricted families. II: Independent case
• Exact bounds for the expectations of order statistics from non-negative populations
• Sharp bounds for expectations of spacings from DDA and DFRA families.
• Projection method for moment bounds on order statistics from restricted families
• Optimal bounds on expectations of order statistics and spacings from nonparametric families of distributions generated by convex transform order
• Non-positive upper bounds on expectations of small order statistics from DDA and DFRA populations
• Projection bounds on expectations of generalized order statistics from DD and DDA families
• Maximal Expectations of Extreme Order Statistics from Increasing Density and Failure Rate Populations
• Optimal bounds for the mean of the total time on test for distributions with decreasing generalized failure rate
• Non-positive upper bounds on expectations of low rank order statistics from DFR populations
• Projection bounds on expectations of generalized order statistics from DFR and DFRA families
• How deviant can you be? The complete solution
• Bounds for Expectations of Differences of Generalized Order Statistics Based on General and Life Distributions
• On Families of Distributions for Which Optimal Bounds on Expectations of GOS Can be Derived
• Projection Bounds on Expectations of Spacings of Generalized Order Statistics from DD and DDA Families
• Projection bounds on expectations of spacings of generalized order statistics from DFR and DFRA families
• Sharp bounds on l-estimates and their expectations for dependent samples
• Sharp upper mean-variance bounds for trimmed means from restricted families
• Optimal mean-variance bounds on order statistics from families determined by star ordering
• Sharp bounds for the mean of the total time on test for distributions with increasing generalized failure rate
• Upper non positive bounds on expectations of generalized order statistics from DD and DDA populations
• Sharp bounds for expectations of spacings from decreasing density and failure rate families
• OPTIMAL MOMENT INEQUALITIES FOR ORDER STATISTICS FROM NONNEGATIVE RANDOM VARIABLES
• Refined solution to upper-bound problem for the expectations of order statistics from decreasing density on the average distributions
• On upper bounds on expectations of gOSs based on DFR and DFRA distributions
• Analytic Inequalities
• LIMITS OF THE RATIO OF MEAN RANGE TO STANDARD DEVIATION
• A Modification of Schwarz's Inequality with Applications to Distributions
• The Maxima of the Mean Largest Value and of the Range
• Universal Bounds for Mean Range and Extreme Observation
• Mean-variance bounds for order statistics from dependent DFR, IFR, DFRA and IFRA samples

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