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/