CDF Inv

Evaluates the Arcsin distribution CDF inverse.

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Interface
CDF Inv
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Interface

C++

Excel

CDF Inv

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

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

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

(2)

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

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 inverse
a	the parameter of the CDF inverse (must be positive)

Returns

the inverse CDF of the Arcsin distribution

Authors

Lucian Bentea (September 2005)

Source Code

Source code is available when you buy a Commercial licence.

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