Documentation

qfuncinv

Inverse Q function

y = qfuncinv(x)

Description

y = qfuncinv(x) returns the argument of the Q function at which the Q function's value is x. The input x must be a real array with elements between 0 and 1, inclusive.

For a scalar x, the Q function is one minus the cumulative distribution function of the standardized normal random variable, evaluated at x. The Q function is defined as

$Q\left(x\right)=\frac{1}{\sqrt{2\pi }}\underset{x}{\overset{\infty }{\int }}\mathrm{exp}\left(-{t}^{2}/2\right)dt$

The Q function is related to the complementary error function, erfc, according to

$Q\left(x\right)=\frac{1}{2}\text{erfc}\left(\frac{x}{\sqrt{2}}\right)$

Examples

The example below illustrates the inverse relationship between qfunc and qfuncinv.

x1 = [0 1 2; 3 4 5];
y1 = qfuncinv(qfunc(x1)) % Invert qfunc to recover x1.
x2 = 0:.2:1;
y2 = qfunc(qfuncinv(x2)) % Invert qfuncinv to recover x2.

The output is below.

y1 =

0     1     2
3     4     5

y2 =

0    0.2000    0.4000    0.6000    0.8000    1.0000