CodeCogs

Evaluates the Arcsin distribution CDF inverse.

View versions (1)

Interface

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

using namespace Statistics::Distributions::Continuous::Arcsin;

inline double CDF_inv(double x, double a)

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

$D^{-1}(x, a) = a \sin \left( \pi x - \frac{\pi}{2} \right) \qquad 0 \leq x \leq 1 \quad a \geq 0$

(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/arcsin/cdf_inv.h>
#include <iostream>
#include <iomanip>

#define PRECISION 17

int main()
{
  std::cout << "The values of the Arcsin CDF inverse with a = 0.6";
  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_inv(x, 0.6);
    std::cout << std::endl;
  }
  return 0;
}

Output

The values of the Arcsin CDF inverse with a = 0.6
x = {0, 0.1, 0.2, ... , 0.7, 0.8} are

x =   0 : -0.59999999999999998
x = 0.1 : -0.57063390977709216
x = 0.2 : -0.48541019662496843
x = 0.3 : -0.35267115137548377
x = 0.4 : -0.18541019662496841
x = 0.5 : 0
x = 0.6 : 0.18541019662496841
x = 0.7 : 0.35267115137548377
x = 0.8 : 0.48541019662496837

Parameters

the argument of the CDF inverse

the parameter of the CDF inverse (must be positive)

Returns

the inverse CDF of the Arcsin distribution

References

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

Interactive Calculator

Result –

CDF_Inv