Current records and record range with some applications |
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Institution: | 1. Department of Mathematics, Faculty of Science, Zagazig University, Zagazig, Egypt;2. Department of Mathematics and Statistics, MSA University, Cairo, Egypt |
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Abstract: | 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. |
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Keywords: | Current records Record range Stopping time Recurrence relations Weak convergence Weibull distribution Positive Weibull distribution Pareto distribution Negative Pareto distribution |
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