# erf | Error functions using cmath in C++

• Difficulty Level : Easy
• Last Updated : 04 Apr, 2018

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:-

1. 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).
2.  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).

 /* C++ code to use erf */#include #include      /* 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

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