Poisson distribution
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In probability theory and statistics, the Poisson distribution is a discrete probability distribution that expresses the probability of a given number of events occurring in a fixed interval of time i
Chewing gum on a sidewalk. The number of pieces on a single tile is approximately Poisson distributed.
Incomplete gamma function
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In mathematics, the upper and lower incomplete gamma functions are types of special functions which arise as solutions to various mathematical problems such as certain integrals.
Poisson distribution
…PMF λ k e − λ k ! CDF Γ ( ⌊ k + 1 ⌋ , λ ) ⌊ k ⌋ ! , !}},} or e − λ ∑ j = 0 ⌊ k ⌋ λ j j ! , or Q ( ⌊ k + 1 ⌋ , λ ) (for k ≥ 0 , where Γ ( x , y ) is the upper incomplete gamma function, ⌊ k ⌋ is the floor function, and Q is the regularized gamma function) Mean λ Median ≈ ⌊ λ + 1 3 − 1 50 λ ⌋ Mode ⌈ λ ⌉ − 1 , ⌊ λ ⌋ Variance λ Skewness…
The upper incomplete gamma function for some values of s: 0 (blue), 1 (red), 2 (green), 3 (orange), 4 (purple).