CDF

Evaluates the Angle distribution CDF.

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CDF
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Interface

C++

Excel

CDF

doubleCDF(	double	`x`
	int	`n`	)[inline]

This component evaluates the CDF of the Angle distribution with given arguments. x is an angle between 0 and $\inline \pi$ , corresponding to the angle made in an n dimensional space, between a fixed line passing through the origin, and an arbitrary line that also passes through the origin, which is specified by choosing any point on the n dimensional sphere with uniform probability.

The Angle CDF is defined by the following formula

$\mathrm{D}(x) = \frac{\Gamma\left(\frac{n}{2}\right)} {\sqrt{\pi} \,\Gamma\left(\frac{n-1}{2}\right)} \int_0^x \sin^{n-2}(t) \mathrm{d}t \qquad \mbox{if } n > 2$

(2)

and

$\mathrm{D}(x) = \frac{x}{\pi} \qquad \mbox{if } n = 2$

(3)

for all

$x \in [0, \pi]$

(4)

The following figure illustrates the typical shape of the Angle distribution for a range of n:

There is an error with your graph parameters for CDF with options x=0:3.5 n=2:6:5

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

Example 1

In the given example, the CDF is evaluated using a fixed value for n, equal to 4, while the first argument x takes values from 0 up to 2 with a step equal to 0.2. The maximum number of precision digits, implicitly set to 17, may be changed through the <em> PRECISION </em> define.

#include <codecogs/stats/dists/continuous/angle/cdf.h>
#include <iostream>
#include <iomanip>
 
#define PRECISION 17
 
int main()
{
  std::cout << "The values of the Angle CDF with n = 4 and";
  std::cout << std::endl;
  std::cout << "x = {0, 0.2, 0.4, ..., 1.8, 2} are" << std::endl;
  std::cout << std::endl;
  for (double x = 0; x < 2.1; x += 0.2)
  {
    std::cout << std::setprecision(2);
    std::cout << "x = " << std::setw(3) << x << " : ";
    std::cout << std::setprecision(PRECISION);
    std::cout << Stats::Dists::Continuous::Angle::CDF(x, 4);
    std::cout << std::endl;
  }
  return 0;
}

Output

The values of the Angle CDF with n = 4 and
x = {0, 0.2, 0.4, ..., 1.8, 2} are
 
x =   0 : 0
x = 0.2 : 0.001684123127684655
x = 0.4 : 0.013153186649778228
x = 0.6 : 0.042647304023738355
x = 0.8 : 0.095560829038801032
x =   1 : 0.1735907059637424
x = 1.2 : 0.27446855935925973
x = 1.4 : 0.39231882068278456
x = 1.6 : 0.51858635136931963
x = 1.8 : 0.64338711110041569
x =   2 : 0.75706863044011896

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
n	the spatial dimension (must be at least 2)

Returns

the value of the Angle CDF evaluated with the given arguments

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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