Central Limit theorems for records

• Autores: Raúl Gouet Bañares, Francisco Javier López Lorente, Gerardo Sanz Sáiz
• Localización: VIII Journées Zaragoza-Pau de Mathématiques Appliquées et de Statistiques / coord. por Manuel Pedro Palacios Latasa, David Trujillo, Juan José Torrens Iñigo, Monique Madaune-Tort, María Cruz López de Silanes Busto, Gerardo Sanz Sáiz, 2003, ISBN 84-7733-720-9, págs. 331-336
• Idioma: inglés
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• Resumen

  • nsider a sequence (Xn) of independent and identically distributed random variables, taking nonnegative integer values and call Xn a record if Xn > max{X1, . . . , Xn-1}. In Gouet et al. (2001), a martingale approach combined with asymptotic results for sums of partial minima was used to derive strong convergence results for the number of records among the first n observations. Now, in this paper we exploit the connection between records and martingales to establish a central limit theorem for the number of records in many discrete distributions, identifying the centering and scaling sequences.