qfuncinv

Inverse Q function

Syntax

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(x)=12πxexp(t2/2)dt

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

Q(x)=12erfc(x2)

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

See Also

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