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

Simulate a compound renewal process with discrete jumps:

Simulate a compound renewal process with continuous jumps:

Process parameters estimation:

Estimate the distribution parameters from sample data:

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:

Simulate:

Mean function:

CompoundRenewalProcess is a jump process:

Compound renewal process is not weakly stationary:

BinomialProcess is a special case of a compound renewal process:

The mean functions agree:

Create empirical covariance functions:

Compare the covariance functions: