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# CDF

Evaluates the Arcsin distribution CDF.
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C++

## CDF

 doubleCDF( double x double a )[inline]
This function evaluates the CDF of the Arcsin distribution with given argument, defined by

$D(x,&space;a)&space;=&space;\frac{1}{2}&space;+&space;\frac{1}{\pi}&space;\arcsin&space;\left(&space;\frac{x}{a}&space;\right)&space;&space;\quad&space;\mbox{for&space;}&space;x&space;\in&space;(-a,&space;a)$

and

$D(x,&space;a)&space;=&space;0&space;\quad&space;\mbox{for&space;}&space;x&space;\leq&space;-a&space;\qquad&space;D(x,&space;a)&space;=&space;1&space;\quad&space;\mbox{for&space;}&space;x&space;\geq&space;a$

There is an error with your graph parameters for CDF with options x=-1:1 a=1

Error Message:Function CDF failed. Ensure that: Invalid C++

### Example 1

In the example that follows, the CDF is evaluated using values from 0 up to 0.8 with a step equal to 0.1. The maximum number of precision digits, implicitly set to 17, may be changed through the <em> PRECISION </em> define.
#include <codecogs/stats/dists/continuous/arcsin/cdf.h>
#include <iostream>
#include <iomanip>

#define PRECISION 17

int main()
{
std::cout << "The values of the Arcsin CDF with a = 0.7 and";
std::cout << std::endl;
std::cout << "x = {0, 0.1, 0.2, ... , 0.7, 0.8} are" << std::endl;
std::cout << std::endl;
for (double x = 0; x < 0.81; x += 0.1)
{
std::cout << std::setprecision(1);
std::cout << "x = " << std::setw(3) << x << " : ";
std::cout << std::setprecision(PRECISION);
std::cout << Stats::Dists::Continuous::Arcsin::CDF(x, 0.7);
std::cout << std::endl;
}
return 0;
}

### Output

The values of the Arcsin CDF with a = 0.7 and
x = {0, 0.1, 0.2, ... , 0.7, 0.8} are

x =   0 : 0.5
x = 0.1 : 0.54562894834298992
x = 0.2 : 0.59223083110566799
x = 0.3 : 0.64098296402862398
x = 0.4 : 0.69361058099470274
x = 0.5 : 0.7532482855711502
x = 0.6 : 0.82776267147847782
x = 0.7 : 1
x = 0.8 : 1

### References

John Burkardt's library of statistical C++ routines, http://www.csit.fsu.edu/~burkardt/cpp_src/prob/prob.html

### Parameters

 x the argument of the CDF a the parameter of the CDF (must be strictly positive)

### Returns

the CDF of the Arcsin distribution

### Authors

Lucian Bentea (September 2005)
##### Source Code

Source code is available when you agree to a GP Licence or buy a Commercial Licence.

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