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Current records and record range with some applications. (English) Zbl 1306.62108

Summary: In a sequence of independent and identically distributed (iid) random variables, the upper (lower) current records and record range are studied. We derive general recurrence relations between the single and product moments for the upper and lower current records based on Weibull and positive Weibull distributions, as well as Pareto and negative Pareto distributions, respectively. Moreover, some asymptotic results for general current records are established. In addition, a recurrence relation and an explicit formula for the moments of record range based on the exponential distribution are given. Finally, numerical examples are presented to illustrate and corroborate theoretical results.

MSC:

62G30 Order statistics; empirical distribution functions
62G20 Asymptotic properties of nonparametric inference
60E05 Probability distributions: general theory
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