Poisson distreebution

Frae Wikipedia
Lowp tae: navigation, rake
Poisson
Probability mass function
Plot o the Poisson PMF
The horizontal axis is the index k, the nummer o occurrences. λ is the expectit value. The function is defined anly at integer values o k. The connectin lines are anly guides for the ee.
Cumulative distribution function
Plot o the Poisson CDF
The horizontal axis is the index k, the number o occurrences. The CDF is discontinuous at the integers o k an flat everywhaur ense acause a variable that is Poisson distreebutit taks on anly integer values.
Parameters λ > 0 (real)
Support k ∈ ℤ*
pmf
CDF

, or , or

(for , whaur is the incomplete gamma function, is the fluir function, an Q is the regularised gamma function)
Mean
Median
Mode
Variance
Skewness
Ex. kurtosis
Entropy

(for large )


MGF
CF
PGF
Fisher information

In probability theory an stateestics, the Poisson distreebution (French pronunciation [pwasɔ̃]), named efter French mathematician Siméon Denis Poisson, is a discrete probability distreebution that expresses the probability o a gien nummer o events occurrin in a fixed interval o time an/or space if thir events occur wi a kent average rate an independently o the time syne the last event.[1]

References[eedit | eedit soorce]

  1. Frank A. Haight (1967). Handbook of the Poisson Distribution. New York: John Wiley & Sons.