Matlab中本身有Q函数,即qfunc() 其反函数是qfuncinv()
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help qfunc
qfunc
Q function
Syntax
y = qfunc(x)
Description
y = qfunc(x) is one minus the cumulative distribution function of the standardized normal random variable,evaluated at each element of the real array x.For a scalar x,the formula is
The Q function is related to the complementary error function,erfc,according to
Examples
The example below computes the Q function on a matrix,element by element.
x = [0 1 2; 3 4 5];
format short e % Switch to floating point format for displays.
y = qfunc(x)
format % Return to default format for displays.
The output is below.
y =
5.0000e-001 1.5866e-001 2.2750e-002
1.3499e-003 3.1671e-005 2.8665e-007
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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