PDF

Interface

PDF

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

The mean of this distribution is given by

In the example that follows, the PDF is evaluated using values from 0 up to 0.8 with a step equal to 0.1. The mean of the distribution, stored as a constant inside the same namespace, is also displayed. 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/pdf.h>
#include <iostream>
#include <iomanip>
 
#define PRECISION 17
 
int main()
{
  std::cout << "The values of the Arcsin PDF 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::PDF(x, 0.7);
    std::cout << std::endl;
  }
  std::cout << std::endl;
  std::cout << "The mean of the Arcsin distribution is";
  std::cout << std::endl;
  std::cout << Stats::Dists::Continuous::Arcsin::mean;
  std::cout << std::endl;
  return 0;
}

Output:

The values of the Arcsin PDF with a = 0.7 and
x = {0, 0.1, 0.2, ... , 0.7, 0.8} are
 
x =   0 : 0.45472840883398669
x = 0.1 : 0.45944074618482678
x = 0.2 : 0.47450836227811805
x = 0.3 : 0.50329212104487042
x = 0.4 : 0.55410638854399263
x = 0.5 : 0.64974733436139687
x = 0.6 : 0.88283278163289547
x = 0.7 : 0
x = 0.8 : 0
 
The mean of the Arcsin distribution is
0

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 PDF
a	the paramater of the PDF (must be strictly positive)

Returns

the PDF 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.

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