SciPy

scipy.special.gdtr

scipy.special.gdtr(a, b, x) = <ufunc 'gdtr'>

Gamma distribution cumulative density function.

Returns the integral from zero to x of the gamma probability density function,

\[F = \int_0^x \frac{a^b}{\Gamma(b)} t^{b-1} e^{-at}\,dt,\]

where \(\Gamma\) is the gamma function.

Parameters:

a : array_like

The rate parameter of the gamma distribution, sometimes denoted \(\beta\) (float). It is also the reciprocal of the scale parameter \(\theta\).

b : array_like

The shape parameter of the gamma distribution, sometimes denoted \(\alpha\) (float).

x : array_like

The quantile (upper limit of integration; float).

Returns:

F : ndarray

The CDF of the gamma distribution with parameters a and b evaluated at x.

See also

gdtrc
1 - CDF of the gamma distribution.

Notes

The evaluation is carried out using the relation to the incomplete gamma integral (regularized gamma function).

Wrapper for the Cephes [R374] routine gdtr.

References

[R374](1, 2) Cephes Mathematical Functions Library, http://www.netlib.org/cephes/index.html

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