CDF

Evaluates the Arcsin distribution CDF.

Controller: CodeCogs

Contents

Interface
CDF
Page Comments

Interface

C++

CDF

doubleCDF(	double	`x`
	double	`a`	)[inline]

This function evaluates the CDF of the Arcsin distribution with given argument, defined by

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

(2)

and

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

(3)

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.

Not a member, then Register with CodeCogs. Already a Member, then Login.