Poisson distribution
(statistics on count of events happening within a given interval)
The Poisson distribution gives the probability of each possible number
of occurrences of an event happening within a given interval,
specifically for events that are independent but happen with a
fixed probability per unit time.
It is named for French mathematician Siméon Denis Poisson.
f(k;λ)
= probability(X = k)
λke-λ
= ——————
k!
- X - random variable which can have any of 0,1,2,...
- k - a specific value that X can take.
- λ - the expected value of X.
- e - Euler's number, 2.718...
- f(k;λ) - function describing the distribution for a given value of λ.
For example, if something occurs on average
1.1 times per second (i.e., λ=1.1),
then the probability of 6 occurrences within some specific second (i.e., k=6)
is:
1.16e-1.1
—————————
6!
(mathematics,statistics,probability)
Further reading:
https://en.wikipedia.org/wiki/Poisson_distribution
https://mathworld.wolfram.com/PoissonDistribution.html
https://www.itl.nist.gov/div898/handbook/eda/section3/eda366j.htm
http://ned.ipac.caltech.edu/level5/Berg/Berg5.html
http://ned.ipac.caltech.edu/level5/Leo/Stats2_2.html
Referenced by page:
photon noise
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