represents a compound Poisson process with rate parameter λ and jump size distribution jdist.
- CompoundPoissonProcess is also known as cumulative Poisson process or Poisson cluster process.
- CompoundPoissonProcess is a continuous-time and continuous-state or discrete-state random process depending on jdist.
- The state at time is given by , where the are independent and identically distributed random variables following jdist and follows PoissonProcess[λ].
- The parameter λ can be any positive real number and jdist can be any univariate distribution.
- CompoundPoissonProcess can be used with such functions as Mean, Variance, and RandomFunction.
Examplesopen allclose all
Basic Examples (2)
Basic Uses (4)
Process Slice Properties (4)
Slice distribution is a CompoundPoissonDistribution:
Shoppers arrive at a newly renovated store according to a Poisson process with a rate of 20 customers per hour. The store promotes this event by giving every customer a gift. The gift has a value that follows a WeibullDistribution with shape parameter 10 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:
Aggregate claims from a risk follow a compound Poisson process with Poisson parameter 200. The claim amount distribution is a Pareto distribution with minimum value parameter 300, shape parameter 3, and location parameter 0. The insurer has effected excess of loss reinsurance with retention level 300. Simulate the claims process for four years:
Properties & Relations (6)
CompoundPoissonProcess is a jump process:
Any slice distribution of Compound Poisson process is a CompoundPoissonDistribution:
Wolfram Research (2012), CompoundPoissonProcess, Wolfram Language function, https://reference.wolfram.com/language/ref/CompoundPoissonProcess.html.
Wolfram Language. 2012. "CompoundPoissonProcess." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/CompoundPoissonProcess.html.
Wolfram Language. (2012). CompoundPoissonProcess. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/CompoundPoissonProcess.html