`scipy.stats._continuous_distns:gamma_gen`

source: /scipy/stats/_continuous_distns.py :3558

Signature

   class     gamma_gen (    momtype    =  1   ,    a    =  None   ,    b    =  None   ,    xtol    =  1e-14   ,    badvalue    =  None   ,    name    =  None   ,    longname    =  None   ,    shapes    =  None   ,    seed    =  None     )

Members

Summary

A gamma continuous random variable.

Extended Summary

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Notes

The probability density function for gamma is:

f (x, a) = \frac{x ^{a - 1} e ^{- x}}{Γ ( a )}

for $x \geq 0$ , $a > 0$ . Here $Γ (a)$ refers to the gamma function.

gamma takes a as a shape parameter for $a$ .

When $a$ is an integer, gamma reduces to the Erlang distribution, and when $a = 1$ to the exponential distribution.

Gamma distributions are sometimes parameterized with two variables, with a probability density function of:

f (x, α, β) = \frac{β ^{α} x ^{α - 1} e ^{- β x}}{Γ ( α )}

Note that this parameterization is equivalent to the above, with scale = 1 / beta.

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Aliases

scipy.stats._continuous_distns.gamma_gen