Article Dans Une Revue Open Journal of Statistics Année : 2011

Fibonacci congruences and applications

René Blacher
  • Fonction : Auteur
  • PersonId : 839815

Résumé

When we consider a congruence T (x) ≡ ax modulo m as a pseudo random number generator, there are several means of ensuring the independence of two successive num- bers. In this report, we show that this dependence depends on the continued fraction expansion of m/a. We deduce that the congruences such that m and a are two successive elements of Fibonacci sequences are those having the weakest dependence. We will use this result to obtain truly random number sequences xn . For that purpose, we will use non-deterministic sequences yn such that the conditional probabilities have Lipschitz coefficients not too large. They are transformed using Fibonacci congruences and we will get by this way sequences xn . These sequences xn admit the IID model for correct model.

Fichier principal
Vignette du fichier
GealRapportFibo.pdf (361.12 Ko) Télécharger le fichier
Origine Fichiers produits par l'(les) auteur(s)
Licence
Loading...

Dates et versions

hal-00587108 , version 1 (19-04-2011)

Licence

Identifiants

Citer

René Blacher. Fibonacci congruences and applications. Open Journal of Statistics, 2011, 1 (2), pp.128-138. ⟨10.4236/ojs.2011.12015⟩. ⟨hal-00587108⟩
390 Consultations
459 Téléchargements

Altmetric

Partager

  • More