cumd_cau.cpp

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/*
 * $Id$
 *
 * Author: David Fournier
 * Copyright (c) 2008-2012 Regents of the University of California
 */
#include <fvar.hpp>

double cumd_cauchy(const double& x)
{
  double t=0.0;
  const double r2=sqrt(2.0);
  t=atan(x/r2);
  return (0.5 + t/PI);
}

double density_cauchy(const double& x)
{
  const double r2=PI*sqrt(2.0);
  return 1./(r2*(1+0.5*x*x));
}

double log_density_cauchy(const double& x)
{
  const double r2=PI*sqrt(2.0);
  return -log(r2*(1+0.5*x*x));
}

double inv_cumd_cauchy(const double& x)
{
  const double r2=sqrt(2.0);
  return (r2*tan(PI*(x-0.5)));
}