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Statements (76)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:stochastic_process
|
| gptkbp:distributedBy |
gptkb:Poisson_distribution
|
| gptkbp:firstDescribed |
1907
|
| gptkbp:generalizes |
renewal process
|
| gptkbp:hasApplication |
biology
genetics earthquake modeling insurance claim modeling modeling arrivals in queues modeling phone call arrivals modeling radioactive decay modeling random events in time modeling web server requests photon detection traffic flow modeling |
| gptkbp:hasProperty |
gptkb:Markov_property
distribution is determined by the number of events in intervals increments over intervals of equal length are identically distributed Poisson distributed number of events cadlag paths covariance is min(s,t) times lambda distribution determined by rate parameter distribution is determined by the rate parameter distribution is infinitely divisible expected value is lambda times t exponential interarrival times finite jumps future evolution depends only on present increasing process increments are Poisson distributed increments over disjoint intervals are independent independent increments independent of past infinite divisibility integer-valued distribution is determined by the sum of independent and identically distributed interarrival times lack of aftereffect martingale property memoryless property no continuous part no drift no fixed discontinuities no negative jumps no simultaneous events orderliness pure jump process right-continuous paths sample paths are step functions starts at zero stationary increments time-homogeneity variance is lambda times t distribution is determined by the interarrival times distribution is determined by the sum of independent Poisson random variables distribution is determined by the sum of independent and identically distributed exponential random variables distribution is determined by the sum of independent and identically distributed Poisson random variables distribution is determined by the sum of independent and stationary increments distribution is determined by the sum of independent exponential random variables distribution is determined by the sum of independent increments distribution is determined by the sum of independent and identically distributed increments |
| gptkbp:hasSpecialCase |
gptkb:stochastic_process
|
| gptkbp:hasType |
homogeneous Poisson process
non-homogeneous Poisson process |
| https://www.w3.org/2000/01/rdf-schema#label |
Poisson process
|
| gptkbp:namedAfter |
gptkb:Siméon_Denis_Poisson
|
| gptkbp:parameter |
lambda
rate parameter |
| gptkbp:usedIn |
gptkb:probability_theory
finance physics queueing theory statistics telecommunications |
| gptkbp:bfsParent |
gptkb:John_Kingman
gptkb:stochastic_process |
| gptkbp:bfsLayer |
4
|