Wolfram Language & System 10.4 (2016)|Legacy Documentation

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represents a compound renewal process with renewal-time distribution rdist and jump size distribution jdist.


  • CompoundRenewalProcess is also known as a renewal-reward process or cumulative renewal process.
  • CompoundRenewalProcess is a continuous-time process with continuous rdist, a discrete-time process for a discrete rdist, a continuous-state process with continuous jdist, and a discrete-state process with discrete jdist.
  • The distribution rdist can be any univariate distribution with non-negative domain. The distribution jdist can be any univariate distribution.
  • The state at time is given by , where the are independent and identically distributed random variables following jdist and follows RenewalProcess[rdist].
  • CompoundRenewalProcess can be used with such functions as Mean, Variance, and RandomFunction.
Introduced in 2012