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STOCHASTIC ORDERINGS OF DISCRETE-TIME PROCESSES AND DISCRETE RECORD VALUES

  • Félix Belzunce (a1), Eva-María Ortega (a2) and José M. Ruiz (a3)
Abstract

Recently, Pellerey, Shaked, and Zinn [6] introduced a discrete-time analogue of the nonhomogeneous Poisson process. The purpose of this article is to provide some results for stochastic comparisons of the epoch times and the interepoch times of those processes. Also, we show the relationships between these processes and discrete record values and we provide several results for discrete weak record values.

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Karlin, S. & Rinot, Y. (1980). Classes of ordering measures and related correlation inequalities. I. Multivariate totally positive distributions. Journal of Multivariate Analysis10: 467498.

Lehman, E.L. (1966). Some concepts of dependence. Annals of Mathematical Statistics37: 11371153.

Pellerey, F., Shaked, M., & Zinn, J. (2000). Non-homogeneous Poisson processes and logconcavity. Probability in the Engineering and Informational Sciences14: 353373.

Shaked, M., Shanthikumar, J.G., & Valdez-Torres, J.B. (1995). Discrete hazard rate functions. Computers and Operations Research22: 391402.

Stepanov, A.V. (1992). Limit theorems for weak records. Theory of Probability and its Applications37: 570574.

Stepanov, A.V. (1993). A characterization theorem for weak records. Theory of Probability and its Applications38: 762764.

Vervaat, W. (1973). Limit theorems for records from discrete distributions. Stochastic Processes and Their Applications1: 317334.

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Probability in the Engineering and Informational Sciences
  • ISSN: 0269-9648
  • EISSN: 1469-8951
  • URL: /core/journals/probability-in-the-engineering-and-informational-sciences
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