Poisson process

GPTKB entity

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