matlab中如何实现Q函数的反函数

Question

如题所述

Answer 1

Matlab中本身有Q函数，即qfunc() 其
反函数是qfuncinv()
help qfuncinv

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

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

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

Answer 2

sqrt(2)*erfcinv（x）