Central limit theorems for the number of records in discrete models
Raúl Gouet, Francisco Javier López, Gerardo Sanz · Advances in Applied Probability · 2005
Consider a sequence ( X n ) of independent and identically distributed random variables taking nonnegative integer values, and call X n a record if X n > max{ X 1 ,…, X n −1 }. By means of martingale arguments it is shown that the counting process of records among the first n observations, suitably centered and scaled, is asymptotically normally distributed.