In mathematics, the
error function (also called the Gauss error function) is a special function (non-elementary) of sigmoid shape that occurs in probability, statistics, and partial differential equations describing diffusion.
It’s the probability that a normal random variable with mean 0 and variance 0.5 take value between [-x, x]. It is denoted by erf(x) and calculated by:-
In
cmath library of C++, error function has been already implemented. There are two such functions:-
-
erf(x) : This inbuilt function calculate the error function for input value of x. Parameter x which can be int or float or double. It return a double which is erf(x).
- erfc(x) : This inbuilt function calculate the complementary of error function for input value of x. Parameter x which can be int or float or double. It return a double which is 1 – erf(x).
#include <iostream>
#include <cmath> /* erf */
using namespace std;
double findProbability( double a)
{
double prob_x_a = erf(a);
return prob_x_a;
}
int main ()
{
double a = 0.25;
cout << "probability that normal r.v "
"X takes value between "
<< -a << " & " << a << " is "
<< findProbability(a) << endl;
return 0;
}
|
Output:
probability that normal r.v X takes value
between -0.25 & 0.25 is 0.276326
Reference :
Wikipedia