doi:10.3390/math10142442engLafuente, MiguelGouet, RaúlLópez, F. JavierSanz, GerardoNear-Record Values in Discrete Random SequencesART-2022-129774Given 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.2022http://zaguan.unizar.es/record/11816010.3390/math10142442http://zaguan.unizar.es/record/118160oai:zaguan.unizar.es:118160Mathematics 10, 14 (2022), 2442byhttp://creativecommons.org/licenses/by/3.0/es/info:eu-repo/semantics/openAccess