# scipy.special.gdtr¶

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

Gamma distribution cumulative distribution 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
aarray_like

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

barray_like

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

xarray_like

The quantile (upper limit of integration; float).

Returns
Fndarray

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 [1] routine gdtr.

References

1

Cephes Mathematical Functions Library, http://www.netlib.org/cephes/

#### Previous topic

scipy.special.fdtridfd

#### Next topic

scipy.special.gdtrc