Weak limits of standardized sums of independent geometrically distributed random variables

Adell, José A. (Universidad de Zaragoza)

Resumen: We consider standardized sums of independent geometrically distributed random variables whose failure probabilities approach the unity. We show that such sums converge in law to a random variable having an infinitely divisible distribution whose characteristic function depends on the values of the Riemann zeta function at integer arguments. This is motivated by a probabilistic representation of the Stirling numbers of the second kind.

Idioma: Inglés

DOI: 10.1016/j.spl.2025.110410

Año: 2025

Publicado en: Statistics & Probability Letters 222 (2025), 110410 [6 pp.]
ISSN: 0167-7152

Tipo y forma: Article (Published version)

Área (Departamento): Área Estadís. Investig. Opera. (Dpto. Métodos Estadísticos)