ndtr

Normal distribution function.

SYNOPSIS:

double x, y, ndtr();
y = ndtr(x);

DESCRIPTION:

Returns the area under the Gaussian probability density function, integrated from minus infinity to x:

x
-
1 | | 2
ndtr(x) = --------- | exp(- t /2) dt
sqrt(2pi) | |
-
-inf.

= (1 + erf(z)) / 2
= erfc(z) / 2

where z = x/sqrt(2).

Computation is via the functions erf and erfc, with care to avoid error amplification in computing exp(-x^2).

ACCURACY:

Relative error:
arithmetic domain # trials peak rms
IEEE -13,0 30000 1.3e-15 2.2e-16


ERROR MESSAGES:

message condition value returned
underflow x > 37.519379347 0.0