y = qfuncinv(x)
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
The Q function is related to the complementary error function, erfc, according to
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