CompoundPoissonProcess

CompoundPoissonProcess[λ,jdist]

represents a compound Poisson process with rate parameter λ and jump size distribution jdist.

Details

  • 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.

Examples

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Basic Examples  (2)

Simulate a compound Poisson process with an exponential jump size distribution:

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Mean and variance functions:

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Scope  (8)

Applications  (2)

Properties & Relations  (5)

See Also

PoissonProcess  RenewalProcess  CompoundRenewalProcess  InhomogeneousPoissonProcess  TransformedDistribution  CompoundPoissonDistribution

Introduced in 2012
(9.0)