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Evaluates the Anglit distribution CDF inverse.

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Interface

#include <codecogs/statistics/distributions/continuous/anglit/cdf_inv.h>

using namespace Statistics::Distributions::Continuous::Anglit;

inline double CDF_inv(double x)

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

$D^{-1}(x) = \frac{1}{2} \arccos (1 - 2x) - \frac{\pi}{4} \qquad 0 \leq x \leq 1$

(1)

In the example that follows, the CDF inverse 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.

Example 1

#include <codecogs/stats/dists/continuous/anglit/cdf_inv.h>
#include <iostream>
#include <iomanip>

#define PRECISION 17

int main()
{
  std::cout << "The values of the Anglit CDF inverse with";
  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::Anglit::CDF_inv(x);
    std::cout << std::endl;
  }
  return 0;
}

Output

The values of the Anglit CDF inverse with
x = {0, 0.1, 0.2, ... , 0.7, 0.8} are

x =   0 : -0.78539816339744828
x = 0.1 : -0.46364760900080609
x = 0.2 : -0.32175055439664213
x = 0.3 : -0.20575842303374392
x = 0.4 : -0.10067896039516533
x = 0.5 : 0
x = 0.6 : 0.10067896039516544
x = 0.7 : 0.20575842303374403
x = 0.8 : 0.32175055439664213

Parameters

the argument of the CDF inverse

Returns

the inverse CDF of the Anglit distribution

References

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

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Result –