International Journal of Stochastic Analysis
Volume 2011 (2011), Article ID 797656, 14 pages
doi:10.1155/2011/797656
Research Article

A 𝑞 -Weibull Counting Process through a Fractional Differential Operator

Kunnummal Muralidharan1 and Seema S. Nair2

1Department of Statistics, Faculty of Science, The Maharajah Sayajirao University of Baroda, Vadodara 390002, India
2Centre for Mathematical Sciences, Pala Campus, Arunapuram P.O., Pala, Kerala-686 574, India

Received 18 December 2010; Accepted 3 February 2011

Academic Editor: Josefa Linares-Perez

Copyright © 2011 Kunnummal Muralidharan and Seema S. Nair. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We use the 𝑞 -Weibull distribution and define a new counting process using the fractional order. As a consequence, we introduce a 𝑞 -process with 𝑞 -Weibull interarrival times. Some interesting special cases are also discussed which leads to a Mittag-Leffler form.