Law of large numbers for delta records

• Autores: Raúl Gouet Bañares , Francisco Javier López Lorente , Gerardo Sanz Sáiz
• Localización: XXXI Congreso Nacional de Estadística e Investigación Operativa ; V Jornadas de Estadística Pública: Murcia, 10-13 de febrero de 2009 : Libro de Actas, 2009, ISBN 978-84-691-8159-1
• Idioma: inglés
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• Resumen

  • Given a sequence of random variables fXn; n  1g and  2 R, an observation Xn is a -record if Xn > maxfX1; : : : ;Xn..1g + . We obtain weak and strong laws of large numbers for the counting process of -records among the rst n observations from a sequence of independent identically distributed random variables. Unlike most of the previous works on record statistics in the literature, dealing only with discrete or continuous models, we consider general distributions for the observations. We also provide examples of applications of our results to common probability distributions.