On the number and sum of near-record observations

DOI10.1239/aap/1127483746zbMath1080.60053OpenAlexW1992834162MaRDI QIDQ5697201

Anthony G. Pakes, Alexei Stepanov, Narayanaswamy Balakrishnan

Publication date: 17 October 2005

Published in: Advances in Applied Probability (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1239/aap/1127483746

zbMATH Keywords

limit theoremrecord timeinsurence claim

Mathematics Subject Classification ID

Order statistics; empirical distribution functions (62G30) Extreme value theory; extremal stochastic processes (60G70)

Related Items (27)

Statistical inference for the geometric distribution based on \(\delta\)-records ⋮ Asymptotic properties of numbers of observations near sample quantiles ⋮ Central Limit Theorem for the Number of Near-Records ⋮ Limit laws for the cumulative number of ties for the maximum in a random sequence ⋮ Asymptotic behavior of the ratio of weak kth records ⋮ Distribution theory of \(\delta\)-record values. Case \(\delta\leq 0\) ⋮ On asymptotic properties of spacings ⋮ On \(\delta\)-record observations: asymptotic rates for the counting process and elements of maximum likelihood estimation ⋮ Asymptotic properties of near Pfeifer records ⋮ Record statistics of a strongly correlated time series: random walks and Lévy flights ⋮ On numbers of observations in random regions determined by records ⋮ Asymptotic properties of numbers of observations in random regions determined by central order statistics ⋮ On the mathematical theory of records ⋮ Distribution theory of \(\delta\)-record values: case \(\delta \geq 0\) ⋮ Limit Theorems for the Counting Process of Near-Records ⋮ Asymptotic normality for the counting process of weak records and \(\delta \)-records in discrete models ⋮ On numbers of observations in random regions determined by records for tail-less populations ⋮ Asymptotic properties of the ratio of order statistics ⋮ On characterization results based on the number of observations near thek-records ⋮ The long-term behavior of number of near-maximum insurance claims ⋮ Numbers of near bivariate record-concomitant observations ⋮ Limit theorems for numbers of near records ⋮ Limiting behavior of the ratio of \(k\)th records ⋮ Approximations of \(\delta\)-record probabilities in i.i.d. and trend models ⋮ Exact and asymptotic properties of δ-records in the linear drift model ⋮ On the point process of near-record values ⋮ Characterizations based on the numbers of near-order statistics

Cites Work

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• A note on the number of records near the maximum
• The asymptotic distribution of sums of records
• Limit laws for the number of near maxima via the Poisson approximation
• The asymptotic probability of a tie for first place
• On the number of maxima in a discrete sample
• A note on the number of maxima in a discrete sample
• On the number of near-maximum insurance claims
• On the number of near-maximum insurance claim under dependence.
• Exact distribution and Fisher information of weak record values.
• Limit theorems for the number and sum of near-maxima for medium tails.
• A necessary and sufficient condition for the existence of the limiting probability of a tie for first place
• Convolution of geometrics and a reliability problem
• A note on the number of observations near an order statistic
• Criteria for convergence of the number of near maxima for long tails
• The number and sum of near-maxima for thin-tailed populations
• Limit Theorems for Weak Records
• ON THE NUMBER OF RECORDS NEAR THE MAXIMUM

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