Uniformly accurate quantile bounds for sums of arbitrary independent random variables

DOI10.1007/s10959-009-0254-2zbMath1210.60045OpenAlexW2000471116MaRDI QIDQ616267

Michael J. Klass, Krzysztof Nowicki

Publication date: 7 January 2011

Published in: Journal of Theoretical Probability (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10959-009-0254-2

zbMATH Keywords

sum of independent random variablesuniversal boundsmaximum of independent random variablesupper quantiles

Mathematics Subject Classification ID

Inequalities; stochastic orderings (60E15) Sums of independent random variables; random walks (60G50) Spaces of measurable functions ((L^p)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.) (46E30)

Related Items (1)

Uniform bounds on the relative error in the approximation of upper quantiles for sums of arbitrary independent random variables

Cites Work

• A method of approximating expectations of functions of sums of independent random variables
• Approximation of partial sums of arbitrary i. i. d. random variables and the precision of the usual exponential upper bound
• Estimation of moments of sums of independent real random variables
• An optimal bound on the tail distribution of the number of recurrences of an event in product spaces
• Lower tail probability estimates for subordinators and nondecreasing random walks
• A symmetrization-desymmetrization procedure for uniformly good approximation of expectations involving arbitrary sums of generalized \(U\)-statistics.
• Measuring the magnitude of sums of independent random variables
• Uniformly accurate quantile bounds via the truncated moment generating function: the symmetric case

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