Approximation of partial sums of arbitrary i. i. d. random variables and the precision of the usual exponential upper bound

DOI10.1214/AOP/1024404520zbMath0891.62007OpenAlexW2018573063MaRDI QIDQ1370234

Marjorie G. Hahn, Michael J. Klass

Publication date: 26 October 1997

Published in: The Annals of Probability (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1214/aop/1024404520

zbMATH Keywords

tail probabilitiesEsscher transformexponential upper boundsapproximation of exceedance levelslocal probability approximations

Mathematics Subject Classification ID

Asymptotic distribution theory in statistics (62E20) Inequalities; stochastic orderings (60E15) Central limit and other weak theorems (60F05) Large deviations (60F10) Approximations to statistical distributions (nonasymptotic) (62E17)

Related Items (4)

Measuring the magnitude of sums of independent random variables ⋮ Uniformly accurate quantile bounds for sums of arbitrary independent random variables ⋮ Uniform bounds on the relative error in the approximation of upper quantiles for sums of arbitrary independent random variables ⋮ Local prelimit theorems and their applications to finance

Cites Work

• Markov additive processes. II: Large deviations
• Strong large deviation and local limit theorems
• Lower tail probability estimates for subordinators and nondecreasing random walks
• Uniform local probability approximations: Improvements on Berry-Esseen
• A One-Sided Analog of Kolmogorov's Inequality
• Probability Inequalities for the Sum of Independent Random Variables
• Exact Exponential Bounds for Sums of Independent Random Variables
• Probability Inequalities for Sums of Bounded Random Variables
• Some Limit Theorems for Large Deviations
• On large deviations
• An application of Fourier methods to the problem of sharpening the Berry-Esseen inequality
• On Asymptotic Expansions for Distribution Functions of Sums of Independent Random Variables
• Probability Inequalities for Sums of Independent Random Variables

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