G. Sanz Sáiz, R. Gouet, F. J. López
Given a parameter $k > 1$, the nth observation of a sequence of nonnegative observations is a geometric record if $X_n > k max(X_1, dots, X_{n-1})$, that is, if $X_n$ is k times greater than all preceding observations. We study the number of geometric records, $N_n$, among the first $n$ observations in a sequence of independent and identically distributed random variables with distribution $F$. We show that $N_n$ increases to a finite random limit for ligth-tailed $F$. For medium and heavy-tailed distributions, we prove that $N_n$ diverges to infinity. In this case, we prove a law of large numbers and provide conditions for asymptotic normality. When we consider the values of geometric records, we find an unexpected relationship with models of paralyzable counters in particle physics. Examples of applications to common families of distributions are also provided.
Palabras clave: geometric records, asymptotic normality, paralyzable counters
Programado
JC7 Procesos estocásticos 2
19 de abril de 2012 12:00
Sala Roma II
