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1 results

  • Renewal processes with random numbers of delays: application to a conception and birth model

  • Kenneth Lange, Norman J. Johnson
  • Journal:
    Journal of Applied Probability / Volume 15 / Issue 2 / June 1978
    Published online by Cambridge University Press:
    14 July 2016, pp. 209-224
    Print publication:
    June 1978

  • Asymptotic formulas and Laplace–Stieltjes transforms are derived for the first two moments of a renewal process with a random number of delays. These are simplified when all the delays follow the same distribution. An asymptotic occupancy result is also derived for two-stage renewal processes with random numbers of delays. As an example, a demographic model of conception and birth is discussed. This model represents the sequence of live births to a woman as a renewal process. If the woman practises birth control after achieving her desired family composition, the renewal process has a random number of delays.