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2 results

  • Random effect bivariate survival models and stochastic comparisons

  • Part of
  • Ramesh C. Gupta, Rameshwar D. Gupta
  • Journal:
    Journal of Applied Probability / Volume 47 / Issue 2 / June 2010
    Published online by Cambridge University Press:
    14 July 2016, pp. 426-440
    Print publication:
    June 2010
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  • In this paper we propose a general bivariate random effect model with special emphasis on frailty models and environmental effect models, and present some stochastic comparisons. The relationship between the conditional and the unconditional hazard gradients are derived and some examples are provided. We investigate how the well-known stochastic orderings between the distributions of two frailties translate into the orderings between the corresponding survival functions. These results are used to obtain the properties of the bivariate multiplicative model and the shared frailty model.

  • On the probability that the kth customer finds an M/M/1 queue empty

  • Part of
  • Harshinder Singh, Rameshwar D. Gupta
  • Journal:
    Advances in Applied Probability / Volume 24 / Issue 1 / March 1992
    Published online by Cambridge University Press:
    01 July 2016, pp. 238-239
    Print publication:
    March 1992
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  • A result relating the probability that kth customer finds the system empty to the distribution of the number of customers served in a busy period, for an M/M/1 queue, has been obtained. This relationship is similar to the relationship between the probability that the queue is empty at time t and the distribution of the length of the busy period.