Cumulative distribution function¶
-
ndtr(x)¶ Returns the area under the Gaussian probability density function, integrated from minus infinity to
x.Parameters: x (float) – a real scalar.
Description¶
Area under the curve:
\[\frac{1}{\sqrt{2 \pi}} \int_{-\infty}^x \exp(-t^2/2) dt\]
Equivalently, we have:
ndtr(x) = ( 1 + erf(z) ) / 2 = erfc(z) / 2
where \(z = x/\sqrt{2}\). Computation is done via the functions
erf() and erfc() with care to avoid error amplification in
computing \(\exp{(-x^2)}\).
Accuracy¶
| x | relative error | |||
|---|---|---|---|---|
| arithmetic | domain | # trials | peak | rms |
| IEEE | -13, 0 | 30000 | 1.3e-15 | 2.2e-16 |
Error messages¶
| message | condition | value returned |
|---|---|---|
| erfc underflow | x > 37.519379347 | 0.0 |