Asymptotic normality for the counting process of weak records and \(\delta \)-records in discrete models

DOI10.3150/07-BEJ6027zbMath1138.60309arXiv0709.0620MaRDI QIDQ2469650

F. Javier López, Gerardo Sanz, Raúl Gouet

Publication date: 6 February 2008

Published in: Bernoulli (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0709.0620

zbMATH Keywords

central limit theoremmartingalerecordweak record

Mathematics Subject Classification ID

Martingales with discrete parameter (60G42) Central limit and other weak theorems (60F05)

Related Items (14)

Statistical inference for the geometric distribution based on \(\delta\)-records ⋮ Central Limit Theorem for the Number of Near-Records ⋮ Exceedances of 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 \(\delta\)-record observations: asymptotic rates for the counting process and elements of maximum likelihood estimation ⋮ Distribution theory of \(\delta\)-record values: case \(\delta \geq 0\) ⋮ Limit Theorems for the Counting Process of Near-Records ⋮ Numbers of near bivariate record-concomitant observations ⋮ Records from stationary observations subject to a random trend ⋮ Laws of large numbers for the number of weak 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

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