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• W2022307167 abstract "Recent work has considered properties of the number of observations Xj, independently drawn from a discrete law, which equal the sample maximum X(n) The natural analogue for continuous laws is the number Kn(a) of observations in the interval (X(n)–a, X(n)], where a > 0. This paper derives general expressions for the law, first moment, and probability generating function of Kn(a), mentioning examples where evaluations can be given. It seeks limit laws for n→ and finds a central limit result when a is fixed and the population law has a finite right extremity. Whenever the population law is attracted to an extremal law, a limit theorem can be found by letting a depend on n in an appropriate manner; thus the limit law is geometric when the extremal law is the Gumbel type. With these results, the paper obtains limit laws for ‘top end’ spacings X(n) - X(n-j) with j fixed." @default.
• W2022307167 created "2016-06-24" @default.
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• W2022307167 date "1997-06-01" @default.
• W2022307167 modified "2023-10-13" @default.
• W2022307167 title "ON THE NUMBER OF RECORDS NEAR THE MAXIMUM" @default.
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• W2022307167 doi "https://doi.org/10.1111/j.1467-842x.1997.tb00534.x" @default.
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