Asymptotic normality for the counting process of weak records and δ-records in discrete models

Raúl Gouet, F. Javier López, Gerardo Sanz

Let $\{X_n,n\ge 1\}$ be a sequence of independent and identically distributed random variables, taking non-negative integer values, and call $X_n$ a $\delta$-record if $X_n>\max\{X_1,...…