PoissonProcess

PoissonProcess[μ]

represents a Poisson process with rate μ.

Details

PoissonProcess is a continuous-time and discrete-state random process.
PoissonProcess at time t is the number of events in the interval 0 to t.
The number of events in the interval 0 to t follows PoissonDistribution[μ t].
The times between events are independent and follow ExponentialDistribution[μ].
PoissonProcess allows μ to be any positive real number.
PoissonProcess can be used with such functions as Mean, PDF, Probability, and RandomFunction.

Examples

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Basic Examples (3)

Simulate a Poisson process:

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Mean and variance functions:

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Covariance function:

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Scope (12)

Applications (14)

Properties & Relations (10)

Neat Examples (1)

See Also

CompoundPoissonProcess InhomogeneousPoissonProcess RenewalProcess CompoundRenewalProcess TelegraphProcess BinomialProcess PoissonDistribution ExponentialDistribution CompoundPoissonDistribution

Related Guides

Introduced in 2012

(9.0)

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