CompoundRenewalProcess

CompoundRenewalProcess[rdist,jdist]

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

Details

  • 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.

Examples

open allclose all

Basic Examples  (1)

Simulate a compound renewal process with gamma renewal times and exponential jumps:

In[1]:=
Click for copyable input
In[2]:=
Click for copyable input
Out[2]=
In[3]:=
Click for copyable input
Out[3]=

Scope  (3)

Applications  (2)

Properties & Relations  (3)

See Also

CompoundPoissonProcess  RenewalProcess  TransformedDistribution

Introduced in 2012
(9.0)