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.
Examplesopen allclose all
Basic Examples (1)
The hourly arrival of shoppers at a newly renovated store follows an Erlang distribution with shape parameter 2 and rate parameter 30. The store promotes this event by giving every customer a gift. The gift has a value that follows a WeibullDistribution with shape parameter 14 and scale parameter 3. Simulate the cost of the gift process during the 12-hour period for which the store is open that day and find the expected total cost to the store:
Simulate the process for 12 hours:
Expected total cost of the gifts given on the inaugural day:
Simulate the distribution of the cost:
Empirical probability density function:
Empirical probability that the store spends between $450 and $600 on the gifts:
Define a random walk process with steps following NormalDistribution:
Properties & Relations (3)
CompoundRenewalProcess is a jump process:
Compound renewal process is not weakly stationary:
BinomialProcess is a special case of a compound renewal process:
Create empirical covariance functions:
Wolfram Research (2012), CompoundRenewalProcess, Wolfram Language function, https://reference.wolfram.com/language/ref/CompoundRenewalProcess.html.
Wolfram Language. 2012. "CompoundRenewalProcess." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/CompoundRenewalProcess.html.
Wolfram Language. (2012). CompoundRenewalProcess. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/CompoundRenewalProcess.html