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1 results

  • On Cox processes and gamma renewal processes

  • Nikos Yannaros
  • Journal:
    Journal of Applied Probability / Volume 25 / Issue 2 / June 1988
    Published online by Cambridge University Press:
    14 July 2016, pp. 423-427
    Print publication:
    June 1988

  • It is shown that the gamma distribution with shape parameter α can be obtained through a p-thinning for every 0 < p < 1, when 0 < α ≦ 1. In the case α > 1, the gamma distribution cannot be obtained through thinning. The class of renewal processes with gamma-distributed times between events is considered. It is shown that an ordinary gamma renewal process is a Cox process if and only if 0 < α ≦ 1. Necessary and sufficient conditions for delayed gamma renewal processes to be Cox are also given. Finally, a short description of the gamma renewal process as a Cox process is given.