Inverse of the cumulative distribution function¶

ndtri(y)¶

Returns the argument x for which the area under the Gaussian probability density function (integrated from minus infinity to x) is equal to y.

Parameters:	y (float) – area under the curve.

Description¶

For small arguments $0 < y < \exp{(-2)}$ , the program computes $z = \sqrt{-2.0 * \log{y}}$ ; then the approximation is

$x = z - \log{(z)}/z - (1/z) P(1/z) / Q(1/z).$

There are two rational functions P/Q, one for $0 < y < \exp{(-32)}$ and the other for $y$ up to $\exp{(-2)}$ . For larger arguments, $w = y - 0.5$ , and

$x/\sqrt{2\pi} = w + w^3 R(w^2)/S(w^2).$

Accuracy¶

			Relative error
arithmetic	domain	# trials	peak	rms
DEC	0.125, 1	5500	9.5e-17	2.1e-17
DEC	6e-39, 0.135	3500	5.7e-17	1.3e-17
IEEE	0.125, 1	20000	7.2e-16	1.3e-16
IEEE	3e-308, 0.135	50000	4.6e-16	9.8e-17

Error messages¶

message	condition	value returned
ndtri domain	x <= 0	-MAXNUM
ndtri domain	x >= 1	MAXNUM

Reference: http://www.netlib.org/cephes/doubldoc.html#ndtri