000118160 001__ 118160
000118160 005__ 20240319080952.0
000118160 0247_ $$2doi$$a10.3390/math10142442
000118160 0248_ $$2sideral$$a129774
000118160 037__ $$aART-2022-129774
000118160 041__ $$aeng
000118160 100__ $$aLafuente, Miguel
000118160 245__ $$aNear-Record Values in Discrete Random Sequences
000118160 260__ $$c2022
000118160 5060_ $$aAccess copy available to the general public$$fUnrestricted
000118160 5203_ $$aGiven 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.
000118160 540__ $$9info:eu-repo/semantics/openAccess$$aby$$uhttp://creativecommons.org/licenses/by/3.0/es/
000118160 590__ $$a2.4$$b2022
000118160 592__ $$a0.446$$b2022
000118160 591__ $$aMATHEMATICS$$b23 / 329 = 0.07$$c2022$$dQ1$$eT1
000118160 593__ $$aComputer Science (miscellaneous)$$c2022$$dQ2
000118160 593__ $$aMathematics (miscellaneous)$$c2022$$dQ2
000118160 593__ $$aEngineering (miscellaneous)$$c2022$$dQ2
000118160 594__ $$a3.5$$b2022
000118160 655_4 $$ainfo:eu-repo/semantics/article$$vinfo:eu-repo/semantics/publishedVersion
000118160 700__ $$aGouet, Raúl
000118160 700__ $$aLópez, F. Javier
000118160 700__ $$aSanz, Gerardo
000118160 773__ $$g10, 14 (2022), 2442$$pMathematics (Basel)$$tMathematics$$x2227-7390
000118160 8564_ $$s410268$$uhttps://zaguan.unizar.es/record/118160/files/texto_completo.pdf$$yVersión publicada
000118160 8564_ $$s2656266$$uhttps://zaguan.unizar.es/record/118160/files/texto_completo.jpg?subformat=icon$$xicon$$yVersión publicada
000118160 909CO $$ooai:zaguan.unizar.es:118160$$particulos$$pdriver
000118160 951__ $$a2024-03-18-13:09:07
000118160 980__ $$aARTICLE