Renewal processes based on generalized Mittag-Leffler waiting times

被引:26
作者
Cahoy, Dexter O. [2 ]
Polito, Federico [1 ]
机构
[1] Univ Turin, Dept Math, I-10124 Turin, Italy
[2] Louisiana Tech Univ, Coll Engn & Sci, Dept Math & Stat, Ruston, LA USA
关键词
Fractional Poisson process; Generalized Mittag-Leffler distribution; Renewal processes; Prabhakar operator; POISSON;
D O I
10.1016/j.cnsns.2012.08.013
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
The fractional Poisson process has recently attracted experts from several fields of study. Its natural generalization of the ordinary Poisson process made the model more appealing for real-world applications. In this paper, we generalized the standard and fractional Poisson processes through the waiting time distribution, and showed their relations to an integral operator with a generalized Mittag-Leffler function in the kernel. The waiting times of the proposed renewal processes have the generalized Mittag-Leffler and stretched-squashed Mittag-Leffler distributions. Note that the generalizations naturally provide greater flexibility in modeling real-life renewal processes. Algorithms to simulate sample paths and to estimate the model parameters are derived. Note also that these procedures are necessary to make these models more usable in practice. State probabilities and other qualitative or quantitative features of the models are also discussed. (C) 2012 Elsevier B.V. All rights reserved.
引用
收藏
页码:639 / 650
页数:12
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