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Integer valued autoregressive processes with generalized discrete Mittag-Leffler marginals

Author

Listed:
  • K. K. Jose

    (Department of Statistics, St. Thomas College, Palai, Mahatma Gandhi University, Kottayam Arunapuram P.O., Kerala, 686574, India)

  • K. D. Mariyamma

    (Department of Statistics, St. Thomas College, Palai, Mahatma Gandhi University, Kottayam Arunapuram P.O., Kerala, 686574, India)

Abstract

In this paper we consider a generalization of discrete Mittag-Leffler distributions. We introduce and study the properties of a new distribution called geometric generalized discrete Mittag-Leffler distribution. Autoregressive processes with geometric generalized discrete Mittag-Leffler distributions are developed and studied. The distributions are further extended to develop a more general class of geometric generalized discrete semi-Mittag-Leffler distributions. The processes are extended to higher orders also. An application with respect to an empirical data on customer arrivals in a bank counter is also given. Various areas of potential applications like human resource development, insect growth, epidemic modeling, industrial risk modeling, insurance and actuaries, town planning etc are also discussed.

Suggested Citation

  • K. K. Jose & K. D. Mariyamma, 2012. "Integer valued autoregressive processes with generalized discrete Mittag-Leffler marginals," Statistica, Department of Statistics, University of Bologna, vol. 72(2), pages 195-209.
    • Handle: RePEc:bot:rivsta:v:72:y:2012:i:2:p:195-209
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