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Stochastic comparisons of nonhomogeneous processes

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  • Belzunce, Félix
  • Lillo Rodríguez, Rosa Elvira
  • Ruiz, José M.
  • Shaked, Moshe

Abstract

The purpose of this paper is to describe various conditions on the parameters of pairs of nonhomogeneous Poisson or birth processes under which the corresponding epoch or inter-epoch times are stochastically ordered in various senses. We derive results involving the usual stochastic order, the multivariate hazard rate order, the multivariate likelihood ratio order, and the multivariate mean residual life order. A sample of applications involving generalized Yule processes, load-sharing models, and minimal repairs in reliability theory, illustrate the usefulness of the new results.

Suggested Citation

  • Belzunce, Félix & Lillo Rodríguez, Rosa Elvira & Ruiz, José M. & Shaked, Moshe, 2000. "Stochastic comparisons of nonhomogeneous processes," DES - Working Papers. Statistics and Econometrics. WS 9866, Universidad Carlos III de Madrid. Departamento de Estadística.
    • Handle: RePEc:cte:wsrepe:9866
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    References listed on IDEAS

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    1. Shanthikumar, J. George & Yao, David D., 1986. "The preservation of likelihood ratio ordering under convolution," Stochastic Processes and their Applications, Elsevier, vol. 23(2), pages 259-267, December.
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    1. Lillo, Rosa E. & Nanda, Asok K. & Shaked, Moshe, 2001. "Preservation of some likelihood ratio stochastic orders by order statistics," Statistics & Probability Letters, Elsevier, vol. 51(2), pages 111-119, January.
    2. Hu, Taizhong & Zhu, Zegang, 2001. "An analytic proof of the preservation of the up-shifted likelihood ratio order under convolutions," Stochastic Processes and their Applications, Elsevier, vol. 95(1), pages 55-61, September.

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    Keywords

    Mean residual life order;

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