Asymptotic normality for the counting process of weak records and δ-records in discrete models
Gouet, Raúl ; López, F. Javier ; Sanz, Gerardo
Bernoulli, Tome 13 (2007) no. 1, p. 754-781 / Harvested from Project Euclid
Text on Project Euclid
PDF
Alt PDF
Let {Xn, n≥1} be a sequence of independent and identically distributed random variables, taking non-negative integer values, and call Xn a δ-record if Xn>max {X1, …, Xn−1}+δ, where δ is an integer constant. We use martingale arguments to show that the counting process of δ-records among the first n observations, suitably centered and scaled, is asymptotically normally distributed for δ≠0. In particular, taking δ=−1 we obtain a central limit theorem for the number of weak records.
Publié le : 2007-08-14
Classification:  Central limit theorem,  martingale,  record,  weak record 
@article{1186503485,
     author = {Gouet, Ra\'ul and L\'opez, F. Javier and Sanz, Gerardo},
     title = {Asymptotic normality for the counting process of weak records and $\delta$-records in discrete models},
     journal = {Bernoulli},
     volume = {13},
     number = {1},
     year = {2007},
     pages = { 754-781},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1186503485}
}

Gouet, Raúl; López, F. Javier; Sanz, Gerardo. Asymptotic normality for the counting process of weak records and δ-records in discrete models. Bernoulli, Tome 13 (2007) no. 1, pp.  754-781. http://gdmltest.u-ga.fr/item/1186503485/