Order statistics for the Cantor-Fibonacci distribution

• Autores: Ligia-Loretta Cristea, Helmut Prodinger
• Localización: Aequationes mathematicae, ISSN 0001-9054, Vol. 73, Nº. 1-2, 2007, págs. 78-91
• Idioma: inglés
• Texto completo no disponible (Saber más ...)
• Resumen

  • The Cantor distribution is a probability distribution whose cumulative distribution function is the Cantor function. It is obtained from strings consisting of letters 0 and 1 and appropriately attaching a value to them. The Cantor¿Fibonacci distribution additionally rejects strings with two adjacent letters 1. A probability model is associated by assuming that each admissible string (word) of length m is equally likely; eventually the limit m ? 8 is considered. In this way, one can work with discrete objects, which might not be strictly necessary, but is easy to understand.

    We assume that n random numbers (values of random strings) are drawn independently. The interest is in order statistics of these n values: the (average of) the smallest resp. largest of them. Recursions are obtained which are evaluated asymptotically.

    Generalisations to the d-smallest resp. d-largest element are also considered.