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gptkbp:instanceOf
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gptkb:stochastic_process
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gptkbp:application
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modeling arrivals in queues
modeling insurance claims
modeling network packet arrivals
modeling phone call arrivals
modeling radioactive decay
modeling random events in time
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gptkbp:characteristic
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exp(lambda t (e^{iu}-1))
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gptkbp:distributionOfIncrements
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gptkb:Poisson_distribution
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gptkbp:firstDescribed
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1907
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gptkbp:generalizes
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gptkb:Bernoulli_process
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gptkbp:hasGenerator
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difference operator
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gptkbp:hasInfinitesimalGenerator
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lambda (f(n+1)-f(n))
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gptkbp:hasInterarrivalTimeDistribution
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gptkb:exponential_distribution
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gptkbp:hasKolmogorovBackwardEquation
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dP/dt = lambda(P(n+1)-P(n))
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gptkbp:hasKolmogorovForwardEquation
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dP/dt = lambda(P(n-1)-P(n))
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gptkbp:hasLaplaceTransform
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exp(lambda t (s-1))
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gptkbp:hasLimitingDistribution
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gptkb:Poisson_distribution
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gptkbp:hasMathematicalExpectation
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lambda * t
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gptkbp:hasProperty
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gptkb:Markov_property
independent increments
stationary increments
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gptkbp:hasSamplePaths
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piecewise constant
right-continuous
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gptkbp:hasSpecialCase
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gptkb:stochastic_process
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gptkbp:hasStateSpace
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non-negative integers
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gptkbp:hasTransitionProbability
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Poisson probability formula
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gptkbp:hasType
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gptkb:compound_Poisson_process
homogeneous Poisson process
non-homogeneous Poisson process
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gptkbp:hasVariance
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lambda * t
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https://www.w3.org/2000/01/rdf-schema#label
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Poisson Processes
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gptkbp:isContinuousTime
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true
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gptkbp:isDiscreteState
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true
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gptkbp:isMemoryless
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true
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gptkbp:namedAfter
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gptkb:Siméon_Denis_Poisson
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gptkbp:parameter
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rate (lambda)
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gptkbp:relatedTo
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gptkb:exponential_distribution
Markov chain
birth process
jump process
renewal process
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gptkbp:usedIn
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gptkb:probability_theory
finance
physics
queueing theory
statistics
telecommunications
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gptkbp:bfsParent
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gptkb:John_Kingman
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gptkbp:bfsLayer
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4
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