The empirical distribution function and strong laws for functions of order statistics of uniform spacings

DOI10.1016/0047-259X(85)90023-5zbMath0581.62046MaRDI QIDQ1067714

Jan Beirlant, Martien C. A. Van Zuijlen

Publication date: 1985

Published in: Journal of Multivariate Analysis (Search for Journal in Brave)

zbMATH Keywords

strong law of large numbersuniform distributionempirical distributionGlivenko-Cantelli theoremuniform spacingsalmost sure boundsfunctions of order statisticsorder spacings

Mathematics Subject Classification ID

Order statistics; empirical distribution functions (62G30) Strong limit theorems (60F15)

Related Items (12)

On functions bounding the empirical distribution of uniform spacings ⋮ The almost sure behavior of maximal and minimal multivariate \(k_ n\)- spacings ⋮ On asymptotic properties of spacings ⋮ Asymptotic results for \(m\)-th exponential spacings ⋮ Asymptotic efficiencies of spacings tests for goodness of fit ⋮ On entropy estimation by \(m\)-spacing method ⋮ Glivenko-Cantelli-type theorems for weighted empirical distribution functions based on uniform spacings ⋮ Strong Limit Theorems for Sums of Logarithms of High Order Spacings ⋮ Strong bounds for multidimensional spacings ⋮ Optimal bandwidth selection for re-substitution entropy estimation ⋮ On normal spacings ⋮ Asymptotic properties of the uppermost and the lowest mth exponential spacings based on records

Cites Work

• Unnamed Item
• Laws of the iterated logarithm for order statistics of uniform spacings
• Empirical distribution functions and functions of order statistics for mixing random variables
• Some concepts of negative dependence
• A law of the iterated logarithm for functions of order statistics
• Properties of the empirical distribution function for independent nonidentically distributed random variables
• On functions bounding the empirical distribution of uniform spacings
• On the logarithms of high-order spacings
• Probability Inequalities for Sums of Bounded Random Variables
• On the Rate of Growth of the Partial Maxima of a Sequence of Independent Identically Distributed Random Variables.

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