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Integrate the gamma distribution
Integrates the gamma distribution 'pdf' to get its 'cdf'.
2024.Jul.03 20:42:51
α   (β = 1) Shape of the (1-parameter) gamma distribution. •
x0 Integration limit (from 0). •
Points     N. of graph points. •
Show values Show the graph coordinates.

Computes the (numerical) integral of the (1-parameter) gamma distribution by the Simpson's rule.

The 1-parameter gamma distribution is f(x; α) = 1 ⁄ Γ(αxα−1 exp(−x) . It is: γ2(x; α, β) = γ1(x ⁄ β; α) ⁄ β . Also, Γ2(x; α, β) = Γ1(x ⁄ β; α) .

(The presence of the gamma function, though used as its LN, may cause overflows for high values of α .)

Draws plots of f (permitting, e.g., to verify the mode) and F.

References: Plate: BagGammaDSimpson

• Wikipedia: Gamma distribution. Here: k = α and θ = β = 1 .

• Keisan Online Calculator: Gamma distribution Calculator (Casio Computer Co., Ltd.).

• GAMMA.DIST function (Microsoft).

• 1710-08-20: Simpson, Thomas († 1761-05-14).

 
 
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Created: 2019-08-20 — Last modified: 2019-08-21