118160 20240319080952.0 doi 10.3390/math10142442 sideral 129774 ART-2022-129774 eng Lafuente, Miguel Near-Record Values in Discrete Random Sequences 2022 Access copy available to the general public Unrestricted Given a sequence (Xn) of random variables, Xn is said to be a near-record if Xn∈(Mn−1−a,Mn−1], where Mn=max{X1,…,Xn} and a>0 is a parameter. We investigate the point process η on [0,∞) of near-record values from an integer-valued, independent and identically distributed sequence, showing that it is a Bernoulli cluster process. We derive the probability generating functional of η and formulas for the expectation, variance and covariance of the counting variables η(A),A⊂[0,∞). We also derive the strong convergence and asymptotic normality of η([0,n]), as n→∞, under mild regularity conditions on the distribution of the observations. For heavy-tailed distributions, with square-summable hazard rates, we prove that η([0,n]) grows to a finite random limit and compute its probability generating function. We present examples of the application of our results to particular distributions, covering a wide range of behaviours in terms of their right tails. info:eu-repo/semantics/openAccess by http://creativecommons.org/licenses/by/3.0/es/ 2.4 2022 MATHEMATICS 23 / 329 = 0.07 2022 Q1 T1 0.446 2022 Computer Science (miscellaneous) 2022 Q2 Mathematics (miscellaneous) 2022 Q2 Engineering (miscellaneous) 2022 Q2 3.5 2022 info:eu-repo/semantics/article info:eu-repo/semantics/publishedVersion Gouet, Raúl López, F. Javier Sanz, Gerardo 10, 14 (2022), 2442 Mathematics (Basel) Mathematics 2227-7390 410268 http://zaguan.unizar.es/record/118160/files/texto_completo.pdf Versión publicada 2656266 http://zaguan.unizar.es/record/118160/files/texto_completo.jpg?subformat=icon icon Versión publicada oai:zaguan.unizar.es:118160 articulos driver 2024-03-18-13:09:07 ARTICLE