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- W3101502698 abstract "Let {Xn, n≥1} be a sequence of independent and identically distributed random variables, taking non-negative integer values, and call Xn a δ-record if Xn>max {X1, …, Xn−1}+δ, where δ is an integer constant. We use martingale arguments to show that the counting process of δ-records among the first n observations, suitably centered and scaled, is asymptotically normally distributed for δ≠0. In particular, taking δ=−1 we obtain a central limit theorem for the number of weak records." @default.
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- W3101502698 date "2007-08-01" @default.
- W3101502698 modified "2023-09-28" @default.
- W3101502698 title "Asymptotic normality for the counting process of weak records and δ-records in discrete models" @default.
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- W3101502698 doi "https://doi.org/10.3150/07-bej6027" @default.
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