/*! \file dist_graphs.cpp
\brief Produces Scalable Vector Graphic (.svg) files for all distributions.
\details These files can be viewed using most browsers,
though MS Internet Explorer requires a plugin from Adobe.
These file can be converted to .png using Inkscape
(see www.inkscape.org) Export Bit option which by default produces
a Portable Network Graphic file with that same filename but .png suffix instead of .svg.
Using Python, generate.sh does this conversion automatically for all .svg files in a folder.
\author John Maddock and Paul A. Bristow
*/
// Copyright John Maddock 2008.
// Copyright Paul A. Bristow 2008, 2009, 2012
// Use, modification and distribution are subject to the
// Boost Software License, Version 1.0. (See accompanying file
// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
#ifdef _MSC_VER
# pragma warning (disable : 4180) // qualifier applied to function type has no meaning; ignored
# pragma warning (disable : 4503) // decorated name length exceeded, name was truncated
# pragma warning (disable : 4512) // assignment operator could not be generated
# pragma warning (disable : 4224) // nonstandard extension used : formal parameter 'function_ptr' was previously defined as a type
# pragma warning (disable : 4127) // conditional expression is constant
#endif
#define BOOST_MATH_OVERFLOW_ERROR_POLICY ignore_error
#include <boost/math/distributions.hpp>
#include <boost/math/tools/roots.hpp>
#include <boost/svg_plot/svg_2d_plot.hpp>
#include <list>
#include <map>
#include <string>
template <class Dist>
struct is_discrete_distribution
: public boost::mpl::false_{};
template<class T, class P>
struct is_discrete_distribution<boost::math::bernoulli_distribution<T,P> >
: public boost::mpl::true_{};
template<class T, class P>
struct is_discrete_distribution<boost::math::binomial_distribution<T,P> >
: public boost::mpl::true_{};
template<class T, class P>
struct is_discrete_distribution<boost::math::negative_binomial_distribution<T,P> >
: public boost::mpl::true_{};
template<class T, class P>
struct is_discrete_distribution<boost::math::poisson_distribution<T,P> >
: public boost::mpl::true_{};
template<class T, class P>
struct is_discrete_distribution<boost::math::hypergeometric_distribution<T,P> >
: public boost::mpl::true_{};
template <class Dist>
struct value_finder
{
value_finder(Dist const& d, typename Dist::value_type v)
: m_dist(d), m_value(v) {}
inline typename Dist::value_type operator()(const typename Dist::value_type& x)
{
return pdf(m_dist, x) - m_value;
}
private:
Dist m_dist;
typename Dist::value_type m_value;
};
template <class Dist>
class distribution_plotter
{
public:
distribution_plotter() : m_pdf(true), m_min_x(0), m_max_x(0), m_min_y(0), m_max_y(0) {}
distribution_plotter(bool pdf) : m_pdf(pdf), m_min_x(0), m_max_x(0), m_min_y(0), m_max_y(0) {}
void add(const Dist& d, const std::string& name)
{
// Add name of distribution to our list for later:
m_distributions.push_back(std::make_pair(name, d));
//
// Get the extent of the distribution from the support:
double a, b;
std::tr1::tie(a, b) = support(d);
//
// PDF maximimum is at the mode (probably):
double mod;
try
{
mod = mode(d);
}
catch(const std::domain_error& )
{ // but if not use the lower limit of support.
mod = a;
}
if((mod <= a) && !is_discrete_distribution<Dist>::value)
{ // Continuous distribution at or below lower limit of support.
double margin = 1e-2; // Margin of 1% (say) to get lowest off the 'end stop'.
if((a != 0) && (fabs(a) > margin))
{
mod = a * (1 + ((a > 0) ? margin : -margin));
}
else
{ // Case of mod near zero?
mod = margin;
}
}
double peek_y = pdf(d, mod);
double min_y = peek_y / 20;
//
// If the extent is "infinite" then find out how large it
// has to be for the PDF to decay to min_y:
//
if(a <= -(std::numeric_limits<double>::max)())
{
boost::uintmax_t max_iter = 500;
double guess = mod;
if((pdf(d, 0) > min_y) || (guess == 0))
guess = -1e-3;
a = boost::math::tools::bracket_and_solve_root(
value_finder<Dist>(d, min_y),
guess,
8.0,
true,
boost::math::tools::eps_tolerance<double>(10),
max_iter).first;
}
if(b >= (std::numeric_limits<double>::max)())
{
boost::uintmax_t max_iter = 500;
double guess = mod;
if(a <= 0)
if((pdf(d, 0) > min_y) || (guess == 0))
guess = 1e-3;
b = boost::math::tools::bracket_and_solve_root(
value_finder<Dist>(d, min_y),
guess,
8.0,
false,
boost::math::tools::eps_tolerance<double>(10),
max_iter).first;
}
//
// Recalculate peek_y and location of mod so that
// it's not too close to one end of the graph:
// otherwise we may be shooting off to infinity.
//
if(!is_discrete_distribution<Dist>::value)
{
if(mod <= a + (b-a)/50)
{
mod = a + (b-a)/50;
}
if(mod >= b - (b-a)/50)
{
mod = b - (b-a)/50;
}
peek_y = pdf(d, mod);
}
//
// Now set our limits:
//
if(peek_y > m_max_y)
m_max_y = peek_y;
if(m_max_x == m_min_x)
{
m_max_x = b;
m_min_x = a;
}
else
{
if(a < m_min_x)
m_min_x = a;
if(b > m_max_x)
m_max_x = b;
}
}
void plot(const std::string& title, const std::string& file)
{
using namespace boost::svg;
static const svg_color colors[5] =
{
darkblue,
darkred,
darkgreen,
darkorange,
chartreuse
};
if(m_pdf == false)
{
m_min_y = 0;
m_max_y = 1;
}
svg_2d_plot plot;
plot.image_x_size(750);
plot.image_y_size(400);
plot.coord_precision(4); // Avoids any visible steps.
plot.title_font_size(20);
plot.legend_title_font_size(15);
plot.title(title);
if((m_distributions.size() == 1) && (m_distributions.begin()->first == ""))
plot.legend_on(false);
else
plot.legend_on(true);
plot.title_on(true);
//plot.x_major_labels_on(true).y_major_labels_on(true);
//double x_delta = (m_max_x - m_min_x) / 10;
double y_delta = (m_max_y - m_min_y) / 10;
if(is_discrete_distribution<Dist>::value)
plot.x_range(m_min_x - 0.5, m_max_x + 0.5)
.y_range(m_min_y, m_max_y + y_delta);
else
plot.x_range(m_min_x, m_max_x)
.y_range(m_min_y, m_max_y + y_delta);
plot.x_label_on(true).x_label("Random Variable");
plot.y_label_on(true).y_label("Probability");
plot.plot_border_color(lightslategray)
.background_border_color(lightslategray)
.legend_border_color(lightslategray)
.legend_background_color(white);
//
// Work out axis tick intervals:
//
double l = std::floor(std::log10((m_max_x - m_min_x) / 10) + 0.5);
double interval = std::pow(10.0, (int)l);
if(((m_max_x - m_min_x) / interval) > 10)
interval *= 5;
if(is_discrete_distribution<Dist>::value)
{
interval = interval > 1 ? std::floor(interval) : 1;
plot.x_num_minor_ticks(0);
}
plot.x_major_interval(interval);
l = std::floor(std::log10((m_max_y - m_min_y) / 10) + 0.5);
interval = std::pow(10.0, (int)l);
if(((m_max_y - m_min_y) / interval) > 10)
interval *= 5;
plot.y_major_interval(interval);
int color_index = 0;
if(!is_discrete_distribution<Dist>::value)
{
//
// Continuous distribution:
//
for(std::list<std::pair<std::string, Dist> >::const_iterator i = m_distributions.begin();
i != m_distributions.end(); ++i)
{
double x = m_min_x;
double interval = (m_max_x - m_min_x) / 200;
std::map<double, double> data;
while(x <= m_max_x)
{
data[x] = m_pdf ? pdf(i->second, x) : cdf(i->second, x);
x += interval;
}
plot.plot(data, i->first)
.line_on(true)
.line_color(colors[color_index])
.line_width(1.)
.shape(none);
//.bezier_on(true) // Bezier can't cope with badly behaved like uniform & triangular.
++color_index;
color_index = color_index % (sizeof(colors)/sizeof(colors[0]));
}
}
else
{
//
// Discrete distribution:
//
double x_width = 0.75 / m_distributions.size();
double x_off = -0.5 * 0.75;
for(std::list<std::pair<std::string, Dist> >::const_iterator i = m_distributions.begin();
i != m_distributions.end(); ++i)
{
double x = ceil(m_min_x);
double interval = 1;
std::map<double, double> data;
while(x <= m_max_x)
{
double p;
try{
p = m_pdf ? pdf(i->second, x) : cdf(i->second, x);
}
catch(const std::domain_error&)
{
p = 0;
}
data[x + x_off] = 0;
data[x + x_off + 0.00001] = p;
data[x + x_off + x_width] = p;
data[x + x_off + x_width + 0.00001] = 0;
x += interval;
}
x_off += x_width;
svg_2d_plot_series& s = plot.plot(data, i->first);
s.line_on(true)
.line_color(colors[color_index])
.line_width(1.)
.shape(none)
.area_fill(colors[color_index]);
++color_index;
color_index = color_index % (sizeof(colors)/sizeof(colors[0]));
}
}
plot.write(file);
}
private:
bool m_pdf;
std::list<std::pair<std::string, Dist> > m_distributions;
double m_min_x, m_max_x, m_min_y, m_max_y;
};
int main()
{
try
{
distribution_plotter<boost::math::gamma_distribution<> >
gamma_plotter;
gamma_plotter.add(boost::math::gamma_distribution<>(0.75), "shape = 0.75");
gamma_plotter.add(boost::math::gamma_distribution<>(1), "shape = 1");
gamma_plotter.add(boost::math::gamma_distribution<>(3), "shape = 3");
gamma_plotter.plot("Gamma Distribution PDF With Scale = 1", "gamma1_pdf.svg");
distribution_plotter<boost::math::gamma_distribution<> >
gamma_plotter2;
gamma_plotter2.add(boost::math::gamma_distribution<>(2, 0.5), "scale = 0.5");
gamma_plotter2.add(boost::math::gamma_distribution<>(2, 1), "scale = 1");
gamma_plotter2.add(boost::math::gamma_distribution<>(2, 2), "scale = 2");
gamma_plotter2.plot("Gamma Distribution PDF With Shape = 2", "gamma2_pdf.svg");
distribution_plotter<boost::math::normal>
normal_plotter;
normal_plotter.add(boost::math::normal(0, 1), "μ = 0, σ = 1");
normal_plotter.add(boost::math::normal(0, 0.5), "μ = 0, σ = 0.5");
normal_plotter.add(boost::math::normal(0, 2), "μ = 0, σ = 2");
normal_plotter.add(boost::math::normal(-1, 1), "μ = -1, σ = 1");
normal_plotter.add(boost::math::normal(1, 1), "μ = 1, σ = 1");
normal_plotter.plot("Normal Distribution PDF", "normal_pdf.svg");
distribution_plotter<boost::math::laplace>
laplace_plotter;
laplace_plotter.add(boost::math::laplace(0, 1), "μ = 0, σ = 1");
laplace_plotter.add(boost::math::laplace(0, 0.5), "μ = 0, σ = 0.5");
laplace_plotter.add(boost::math::laplace(0, 2), "μ = 0, σ = 2");
laplace_plotter.add(boost::math::laplace(-1, 1), "μ = -1, σ = 1");
laplace_plotter.add(boost::math::laplace(1, 1), "μ = 1, σ = 1");
laplace_plotter.plot("Laplace Distribution PDF", "laplace_pdf.svg");
distribution_plotter<boost::math::non_central_chi_squared>
nc_cs_plotter;
nc_cs_plotter.add(boost::math::non_central_chi_squared(20, 0), "v=20, λ=0");
nc_cs_plotter.add(boost::math::non_central_chi_squared(20, 1), "v=20, λ=1");
nc_cs_plotter.add(boost::math::non_central_chi_squared(20, 5), "v=20, λ=5");
nc_cs_plotter.add(boost::math::non_central_chi_squared(20, 10), "v=20, λ=10");
nc_cs_plotter.add(boost::math::non_central_chi_squared(20, 20), "v=20, λ=20");
nc_cs_plotter.add(boost::math::non_central_chi_squared(20, 100), "v=20, λ=100");
nc_cs_plotter.plot("Non Central Chi Squared PDF", "nccs_pdf.svg");
distribution_plotter<boost::math::non_central_beta>
nc_beta_plotter;
nc_beta_plotter.add(boost::math::non_central_beta(10, 15, 0), "α=10, β=15, δ=0");
nc_beta_plotter.add(boost::math::non_central_beta(10, 15, 1), "α=10, β=15, δ=1");
nc_beta_plotter.add(boost::math::non_central_beta(10, 15, 5), "α=10, β=15, δ=5");
nc_beta_plotter.add(boost::math::non_central_beta(10, 15, 10), "α=10, β=15, δ=10");
nc_beta_plotter.add(boost::math::non_central_beta(10, 15, 40), "α=10, β=15, δ=40");
nc_beta_plotter.add(boost::math::non_central_beta(10, 15, 100), "α=10, β=15, δ=100");
nc_beta_plotter.plot("Non Central Beta PDF", "nc_beta_pdf.svg");
distribution_plotter<boost::math::non_central_f>
nc_f_plotter;
nc_f_plotter.add(boost::math::non_central_f(10, 20, 0), "v1=10, v2=20, λ=0");
nc_f_plotter.add(boost::math::non_central_f(10, 20, 1), "v1=10, v2=20, λ=1");
nc_f_plotter.add(boost::math::non_central_f(10, 20, 5), "v1=10, v2=20, λ=5");
nc_f_plotter.add(boost::math::non_central_f(10, 20, 10), "v1=10, v2=20, λ=10");
nc_f_plotter.add(boost::math::non_central_f(10, 20, 40), "v1=10, v2=20, λ=40");
nc_f_plotter.add(boost::math::non_central_f(10, 20, 100), "v1=10, v2=20, λ=100");
nc_f_plotter.plot("Non Central F PDF", "nc_f_pdf.svg");
distribution_plotter<boost::math::non_central_t>
nc_t_plotter;
nc_t_plotter.add(boost::math::non_central_t(10, -10), "v=10, δ=-10");
nc_t_plotter.add(boost::math::non_central_t(10, -5), "v=10, δ=-5");
nc_t_plotter.add(boost::math::non_central_t(10, 0), "v=10, δ=0");
nc_t_plotter.add(boost::math::non_central_t(10, 5), "v=10, δ=5");
nc_t_plotter.add(boost::math::non_central_t(10, 10), "v=10, δ=10");
nc_t_plotter.add(boost::math::non_central_t(std::numeric_limits<double>::infinity(), 15), "v=inf, δ=15");
nc_t_plotter.plot("Non Central T PDF", "nc_t_pdf.svg");
distribution_plotter<boost::math::non_central_t>
nc_t_CDF_plotter(false);
nc_t_CDF_plotter.add(boost::math::non_central_t(10, -10), "v=10, δ=-10");
nc_t_CDF_plotter.add(boost::math::non_central_t(10, -5), "v=10, δ=-5");
nc_t_CDF_plotter.add(boost::math::non_central_t(10, 0), "v=10, δ=0");
nc_t_CDF_plotter.add(boost::math::non_central_t(10, 5), "v=10, δ=5");
nc_t_CDF_plotter.add(boost::math::non_central_t(10, 10), "v=10, δ=10");
nc_t_CDF_plotter.add(boost::math::non_central_t(std::numeric_limits<double>::infinity(), 15), "v=inf, δ=15");
nc_t_CDF_plotter.plot("Non Central T CDF", "nc_t_cdf.svg");
distribution_plotter<boost::math::beta_distribution<> >
beta_plotter;
beta_plotter.add(boost::math::beta_distribution<>(0.5, 0.5), "alpha=0.5, beta=0.5");
beta_plotter.add(boost::math::beta_distribution<>(5, 1), "alpha=5, beta=1");
beta_plotter.add(boost::math::beta_distribution<>(1, 3), "alpha=1, beta=3");
beta_plotter.add(boost::math::beta_distribution<>(2, 2), "alpha=2, beta=2");
beta_plotter.add(boost::math::beta_distribution<>(2, 5), "alpha=2, beta=5");
beta_plotter.plot("Beta Distribution PDF", "beta_pdf.svg");
distribution_plotter<boost::math::cauchy_distribution<> >
cauchy_plotter;
cauchy_plotter.add(boost::math::cauchy_distribution<>(-5, 1), "location = -5");
cauchy_plotter.add(boost::math::cauchy_distribution<>(0, 1), "location = 0");
cauchy_plotter.add(boost::math::cauchy_distribution<>(5, 1), "location = 5");
cauchy_plotter.plot("Cauchy Distribution PDF (scale = 1)", "cauchy_pdf1.svg");
distribution_plotter<boost::math::cauchy_distribution<> >
cauchy_plotter2;
cauchy_plotter2.add(boost::math::cauchy_distribution<>(0, 0.5), "scale = 0.5");
cauchy_plotter2.add(boost::math::cauchy_distribution<>(0, 1), "scale = 1");
cauchy_plotter2.add(boost::math::cauchy_distribution<>(0, 2), "scale = 2");
cauchy_plotter2.plot("Cauchy Distribution PDF (location = 0)", "cauchy_pdf2.svg");
distribution_plotter<boost::math::chi_squared_distribution<> >
chi_squared_plotter;
//chi_squared_plotter.add(boost::math::chi_squared_distribution<>(1), "v=1");
chi_squared_plotter.add(boost::math::chi_squared_distribution<>(2), "v=2");
chi_squared_plotter.add(boost::math::chi_squared_distribution<>(5), "v=5");
chi_squared_plotter.add(boost::math::chi_squared_distribution<>(10), "v=10");
chi_squared_plotter.plot("Chi Squared Distribution PDF", "chi_squared_pdf.svg");
distribution_plotter<boost::math::exponential_distribution<> >
exponential_plotter;
exponential_plotter.add(boost::math::exponential_distribution<>(0.5), "λ=0.5");
exponential_plotter.add(boost::math::exponential_distribution<>(1), "λ=1");
exponential_plotter.add(boost::math::exponential_distribution<>(2), "λ=2");
exponential_plotter.plot("Exponential Distribution PDF", "exponential_pdf.svg");
distribution_plotter<boost::math::extreme_value_distribution<> >
extreme_value_plotter;
extreme_value_plotter.add(boost::math::extreme_value_distribution<>(-5), "location=-5");
extreme_value_plotter.add(boost::math::extreme_value_distribution<>(0), "location=0");
extreme_value_plotter.add(boost::math::extreme_value_distribution<>(5), "location=5");
extreme_value_plotter.plot("Extreme Value Distribution PDF (shape=1)", "extreme_value_pdf1.svg");
distribution_plotter<boost::math::extreme_value_distribution<> >
extreme_value_plotter2;
extreme_value_plotter2.add(boost::math::extreme_value_distribution<>(0, 0.5), "shape=0.5");
extreme_value_plotter2.add(boost::math::extreme_value_distribution<>(0, 1), "shape=1");
extreme_value_plotter2.add(boost::math::extreme_value_distribution<>(0, 2), "shape=2");
extreme_value_plotter2.plot("Extreme Value Distribution PDF (location=0)", "extreme_value_pdf2.svg");
distribution_plotter<boost::math::fisher_f_distribution<> >
fisher_f_plotter;
fisher_f_plotter.add(boost::math::fisher_f_distribution<>(4, 4), "n=4, m=4");
fisher_f_plotter.add(boost::math::fisher_f_distribution<>(10, 4), "n=10, m=4");
fisher_f_plotter.add(boost::math::fisher_f_distribution<>(10, 10), "n=10, m=10");
fisher_f_plotter.add(boost::math::fisher_f_distribution<>(4, 10), "n=4, m=10");
fisher_f_plotter.plot("F Distribution PDF", "fisher_f_pdf.svg");
distribution_plotter<boost::math::lognormal_distribution<> >
lognormal_plotter;
lognormal_plotter.add(boost::math::lognormal_distribution<>(-1), "location=-1");
lognormal_plotter.add(boost::math::lognormal_distribution<>(0), "location=0");
lognormal_plotter.add(boost::math::lognormal_distribution<>(1), "location=1");
lognormal_plotter.plot("Lognormal Distribution PDF (scale=1)", "lognormal_pdf1.svg");
distribution_plotter<boost::math::lognormal_distribution<> >
lognormal_plotter2;
lognormal_plotter2.add(boost::math::lognormal_distribution<>(0, 0.5), "scale=0.5");
lognormal_plotter2.add(boost::math::lognormal_distribution<>(0, 1), "scale=1");
lognormal_plotter2.add(boost::math::lognormal_distribution<>(0, 2), "scale=2");
lognormal_plotter2.plot("Lognormal Distribution PDF (location=0)", "lognormal_pdf2.svg");
distribution_plotter<boost::math::pareto_distribution<> >
pareto_plotter; // Rely on 2nd parameter shape = 1 default.
pareto_plotter.add(boost::math::pareto_distribution<>(1), "scale=1");
pareto_plotter.add(boost::math::pareto_distribution<>(2), "scale=2");
pareto_plotter.add(boost::math::pareto_distribution<>(3), "scale=3");
pareto_plotter.plot("Pareto Distribution PDF (shape=1)", "pareto_pdf1.svg");
distribution_plotter<boost::math::pareto_distribution<> >
pareto_plotter2;
pareto_plotter2.add(boost::math::pareto_distribution<>(1, 0.5), "shape=0.5");
pareto_plotter2.add(boost::math::pareto_distribution<>(1, 1), "shape=1");
pareto_plotter2.add(boost::math::pareto_distribution<>(1, 2), "shape=2");
pareto_plotter2.plot("Pareto Distribution PDF (scale=1)", "pareto_pdf2.svg");
distribution_plotter<boost::math::rayleigh_distribution<> >
rayleigh_plotter;
rayleigh_plotter.add(boost::math::rayleigh_distribution<>(0.5), "σ=0.5");
rayleigh_plotter.add(boost::math::rayleigh_distribution<>(1), "σ=1");
rayleigh_plotter.add(boost::math::rayleigh_distribution<>(2), "σ=2");
rayleigh_plotter.add(boost::math::rayleigh_distribution<>(4), "σ=4");
rayleigh_plotter.add(boost::math::rayleigh_distribution<>(10), "σ=10");
rayleigh_plotter.plot("Rayleigh Distribution PDF", "rayleigh_pdf.svg");
distribution_plotter<boost::math::rayleigh_distribution<> >
rayleigh_cdf_plotter(false);
rayleigh_cdf_plotter.add(boost::math::rayleigh_distribution<>(0.5), "σ=0.5");
rayleigh_cdf_plotter.add(boost::math::rayleigh_distribution<>(1), "σ=1");
rayleigh_cdf_plotter.add(boost::math::rayleigh_distribution<>(2), "σ=2");
rayleigh_cdf_plotter.add(boost::math::rayleigh_distribution<>(4), "σ=4");
rayleigh_cdf_plotter.add(boost::math::rayleigh_distribution<>(10), "σ=10");
rayleigh_cdf_plotter.plot("Rayleigh Distribution CDF", "rayleigh_cdf.svg");
distribution_plotter<boost::math::skew_normal_distribution<> >
skew_normal_plotter;
skew_normal_plotter.add(boost::math::skew_normal_distribution<>(0,1,0), "{0,1,0}");
skew_normal_plotter.add(boost::math::skew_normal_distribution<>(0,1,1), "{0,1,1}");
skew_normal_plotter.add(boost::math::skew_normal_distribution<>(0,1,4), "{0,1,4}");
skew_normal_plotter.add(boost::math::skew_normal_distribution<>(0,1,20), "{0,1,20}");
skew_normal_plotter.add(boost::math::skew_normal_distribution<>(0,1,-2), "{0,1,-2}");
skew_normal_plotter.add(boost::math::skew_normal_distribution<>(-2,0.5,-1), "{-2,0.5,-1}");
skew_normal_plotter.plot("Skew Normal Distribution PDF", "skew_normal_pdf.svg");
distribution_plotter<boost::math::skew_normal_distribution<> >
skew_normal_cdf_plotter(false);
skew_normal_cdf_plotter.add(boost::math::skew_normal_distribution<>(0,1,0), "{0,1,0}");
skew_normal_cdf_plotter.add(boost::math::skew_normal_distribution<>(0,1,1), "{0,1,1}");
skew_normal_cdf_plotter.add(boost::math::skew_normal_distribution<>(0,1,4), "{0,1,4}");
skew_normal_cdf_plotter.add(boost::math::skew_normal_distribution<>(0,1,20), "{0,1,20}");
skew_normal_cdf_plotter.add(boost::math::skew_normal_distribution<>(0,1,-2), "{0,1,-2}");
skew_normal_cdf_plotter.add(boost::math::skew_normal_distribution<>(-2,0.5,-1), "{-2,0.5,-1}");
skew_normal_cdf_plotter.plot("Skew Normal Distribution CDF", "skew_normal_cdf.svg");
distribution_plotter<boost::math::triangular_distribution<> >
triangular_plotter;
triangular_plotter.add(boost::math::triangular_distribution<>(-1,0,1), "{-1,0,1}");
triangular_plotter.add(boost::math::triangular_distribution<>(0,1,1), "{0,1,1}");
triangular_plotter.add(boost::math::triangular_distribution<>(0,1,3), "{0,1,3}");
triangular_plotter.add(boost::math::triangular_distribution<>(0,0.5,1), "{0,0.5,1}");
triangular_plotter.add(boost::math::triangular_distribution<>(-2,0,3), "{-2,0,3}");
triangular_plotter.plot("Triangular Distribution PDF", "triangular_pdf.svg");
distribution_plotter<boost::math::triangular_distribution<> >
triangular_cdf_plotter(false);
triangular_cdf_plotter.add(boost::math::triangular_distribution<>(-1,0,1), "{-1,0,1}");
triangular_cdf_plotter.add(boost::math::triangular_distribution<>(0,1,1), "{0,1,1}");
triangular_cdf_plotter.add(boost::math::triangular_distribution<>(0,1,3), "{0,1,3}");
triangular_cdf_plotter.add(boost::math::triangular_distribution<>(0,0.5,1), "{0,0.5,1}");
triangular_cdf_plotter.add(boost::math::triangular_distribution<>(-2,0,3), "{-2,0,3}");
triangular_cdf_plotter.plot("Triangular Distribution CDF", "triangular_cdf.svg");
distribution_plotter<boost::math::students_t_distribution<> >
students_t_plotter;
students_t_plotter.add(boost::math::students_t_distribution<>(1), "v=1");
students_t_plotter.add(boost::math::students_t_distribution<>(5), "v=5");
students_t_plotter.add(boost::math::students_t_distribution<>(30), "v=30");
students_t_plotter.plot("Students T Distribution PDF", "students_t_pdf.svg");
distribution_plotter<boost::math::weibull_distribution<> >
weibull_plotter;
weibull_plotter.add(boost::math::weibull_distribution<>(0.75), "shape=0.75");
weibull_plotter.add(boost::math::weibull_distribution<>(1), "shape=1");
weibull_plotter.add(boost::math::weibull_distribution<>(5), "shape=5");
weibull_plotter.add(boost::math::weibull_distribution<>(10), "shape=10");
weibull_plotter.plot("Weibull Distribution PDF (scale=1)", "weibull_pdf1.svg");
distribution_plotter<boost::math::weibull_distribution<> >
weibull_plotter2;
weibull_plotter2.add(boost::math::weibull_distribution<>(3, 0.5), "scale=0.5");
weibull_plotter2.add(boost::math::weibull_distribution<>(3, 1), "scale=1");
weibull_plotter2.add(boost::math::weibull_distribution<>(3, 2), "scale=2");
weibull_plotter2.plot("Weibull Distribution PDF (shape=3)", "weibull_pdf2.svg");
distribution_plotter<boost::math::uniform_distribution<> >
uniform_plotter;
uniform_plotter.add(boost::math::uniform_distribution<>(0, 1), "{0,1}");
uniform_plotter.add(boost::math::uniform_distribution<>(0, 3), "{0,3}");
uniform_plotter.add(boost::math::uniform_distribution<>(-2, 3), "{-2,3}");
uniform_plotter.add(boost::math::uniform_distribution<>(-1, 1), "{-1,1}");
uniform_plotter.plot("Uniform Distribution PDF", "uniform_pdf.svg");
distribution_plotter<boost::math::uniform_distribution<> >
uniform_cdf_plotter(false);
uniform_cdf_plotter.add(boost::math::uniform_distribution<>(0, 1), "{0,1}");
uniform_cdf_plotter.add(boost::math::uniform_distribution<>(0, 3), "{0,3}");
uniform_cdf_plotter.add(boost::math::uniform_distribution<>(-2, 3), "{-2,3}");
uniform_cdf_plotter.add(boost::math::uniform_distribution<>(-1, 1), "{-1,1}");
uniform_cdf_plotter.plot("Uniform Distribution CDF", "uniform_cdf.svg");
distribution_plotter<boost::math::bernoulli_distribution<> >
bernoulli_plotter;
bernoulli_plotter.add(boost::math::bernoulli_distribution<>(0.25), "p=0.25");
bernoulli_plotter.add(boost::math::bernoulli_distribution<>(0.5), "p=0.5");
bernoulli_plotter.add(boost::math::bernoulli_distribution<>(0.75), "p=0.75");
bernoulli_plotter.plot("Bernoulli Distribution PDF", "bernoulli_pdf.svg");
distribution_plotter<boost::math::bernoulli_distribution<> >
bernoulli_cdf_plotter(false);
bernoulli_cdf_plotter.add(boost::math::bernoulli_distribution<>(0.25), "p=0.25");
bernoulli_cdf_plotter.add(boost::math::bernoulli_distribution<>(0.5), "p=0.5");
bernoulli_cdf_plotter.add(boost::math::bernoulli_distribution<>(0.75), "p=0.75");
bernoulli_cdf_plotter.plot("Bernoulli Distribution CDF", "bernoulli_cdf.svg");
distribution_plotter<boost::math::binomial_distribution<> >
binomial_plotter;
binomial_plotter.add(boost::math::binomial_distribution<>(5, 0.5), "n=5 p=0.5");
binomial_plotter.add(boost::math::binomial_distribution<>(20, 0.5), "n=20 p=0.5");
binomial_plotter.add(boost::math::binomial_distribution<>(50, 0.5), "n=50 p=0.5");
binomial_plotter.plot("Binomial Distribution PDF", "binomial_pdf_1.svg");
distribution_plotter<boost::math::binomial_distribution<> >
binomial_plotter2;
binomial_plotter2.add(boost::math::binomial_distribution<>(20, 0.1), "n=20 p=0.1");
binomial_plotter2.add(boost::math::binomial_distribution<>(20, 0.5), "n=20 p=0.5");
binomial_plotter2.add(boost::math::binomial_distribution<>(20, 0.9), "n=20 p=0.9");
binomial_plotter2.plot("Binomial Distribution PDF", "binomial_pdf_2.svg");
distribution_plotter<boost::math::negative_binomial_distribution<> >
negative_binomial_plotter;
negative_binomial_plotter.add(boost::math::negative_binomial_distribution<>(20, 0.25), "n=20 p=0.25");
negative_binomial_plotter.add(boost::math::negative_binomial_distribution<>(20, 0.5), "n=20 p=0.5");
negative_binomial_plotter.add(boost::math::negative_binomial_distribution<>(20, 0.75), "n=20 p=0.75");
negative_binomial_plotter.plot("Negative Binomial Distribution PDF", "negative_binomial_pdf_1.svg");
distribution_plotter<boost::math::negative_binomial_distribution<> >
negative_binomial_plotter2;
negative_binomial_plotter2.add(boost::math::negative_binomial_distribution<>(10, 0.5), "n=10 p=0.5");
negative_binomial_plotter2.add(boost::math::negative_binomial_distribution<>(20, 0.5), "n=20 p=0.5");
negative_binomial_plotter2.add(boost::math::negative_binomial_distribution<>(70, 0.5), "n=70 p=0.5");
negative_binomial_plotter2.plot("Negative Binomial Distribution PDF", "negative_binomial_pdf_2.svg");
distribution_plotter<boost::math::poisson_distribution<> >
poisson_plotter;
poisson_plotter.add(boost::math::poisson_distribution<>(5), "λ=5");
poisson_plotter.add(boost::math::poisson_distribution<>(10), "λ=10");
poisson_plotter.add(boost::math::poisson_distribution<>(20), "λ=20");
poisson_plotter.plot("Poisson Distribution PDF", "poisson_pdf_1.svg");
distribution_plotter<boost::math::hypergeometric_distribution<> >
hypergeometric_plotter;
hypergeometric_plotter.add(boost::math::hypergeometric_distribution<>(30, 50, 500), "N=500, r=50, n=30");
hypergeometric_plotter.add(boost::math::hypergeometric_distribution<>(30, 100, 500), "N=500, r=100, n=30");
hypergeometric_plotter.add(boost::math::hypergeometric_distribution<>(30, 250, 500), "N=500, r=250, n=30");
hypergeometric_plotter.add(boost::math::hypergeometric_distribution<>(30, 400, 500), "N=500, r=400, n=30");
hypergeometric_plotter.add(boost::math::hypergeometric_distribution<>(30, 450, 500), "N=500, r=450, n=30");
hypergeometric_plotter.plot("Hypergeometric Distribution PDF", "hypergeometric_pdf_1.svg");
distribution_plotter<boost::math::hypergeometric_distribution<> >
hypergeometric_plotter2;
hypergeometric_plotter2.add(boost::math::hypergeometric_distribution<>(50, 50, 500), "N=500, r=50, n=50");
hypergeometric_plotter2.add(boost::math::hypergeometric_distribution<>(100, 50, 500), "N=500, r=50, n=100");
hypergeometric_plotter2.add(boost::math::hypergeometric_distribution<>(250, 50, 500), "N=500, r=50, n=250");
hypergeometric_plotter2.add(boost::math::hypergeometric_distribution<>(400, 50, 500), "N=500, r=50, n=400");
hypergeometric_plotter2.add(boost::math::hypergeometric_distribution<>(450, 50, 500), "N=500, r=50, n=450");
hypergeometric_plotter2.plot("Hypergeometric Distribution PDF", "hypergeometric_pdf_2.svg");
}
catch (std::exception ex)
{
std::cout << ex.what() << std::endl;
}
/* these graphs for hyperexponential distribution not used.
distribution_plotter<boost::math::hyperexponential_distribution<> >
hyperexponential_plotter;
{
const double probs1_1[] = {1.0};
const double rates1_1[] = {1.0};
hyperexponential_plotter.add(boost::math::hyperexponential_distribution<>(probs1_1,rates1_1), "α=(1.0), λ=(1.0)");
const double probs2_1[] = {0.1,0.9};
const double rates2_1[] = {0.5,1.5};
hyperexponential_plotter.add(boost::math::hyperexponential_distribution<>(probs2_1,rates2_1), "α=(0.1,0.9), λ=(0.5,1.5)");
const double probs2_2[] = {0.9,0.1};
const double rates2_2[] = {0.5,1.5};
hyperexponential_plotter.add(boost::math::hyperexponential_distribution<>(probs2_2,rates2_2), "α=(0.9,0.1), λ=(0.5,1.5)");
const double probs3_1[] = {0.2,0.3,0.5};
const double rates3_1[] = {0.5,1.0,1.5};
hyperexponential_plotter.add(boost::math::hyperexponential_distribution<>(probs3_1,rates3_1), "α=(0.2,0.3,0.5), λ=(0.5,1.0,1.5)");
const double probs3_2[] = {0.5,0.3,0.2};
const double rates3_2[] = {0.5,1.0,1.5};
hyperexponential_plotter.add(boost::math::hyperexponential_distribution<>(probs3_1,rates3_1), "α=(0.5,0.3,0.2), λ=(0.5,1.0,1.5)");
}
hyperexponential_plotter.plot("Hyperexponential Distribution PDF", "hyperexponential_pdf.svg");
distribution_plotter<boost::math::hyperexponential_distribution<> >
hyperexponential_plotter2;
{
const double rates[] = {0.5,1.5};
const double probs1[] = {0.1,0.9};
hyperexponential_plotter2.add(boost::math::hyperexponential_distribution<>(probs1,rates), "α=(0.1,0.9), λ=(0.5,1.5)");
const double probs2[] = {0.6,0.4};
hyperexponential_plotter2.add(boost::math::hyperexponential_distribution<>(probs2,rates), "α=(0.6,0.4), λ=(0.5,1.5)");
const double probs3[] = {0.9,0.1};
hyperexponential_plotter2.add(boost::math::hyperexponential_distribution<>(probs3,rates), "α=(0.9,0.1), λ=(0.5,1.5)");
}
hyperexponential_plotter2.plot("Hyperexponential Distribution PDF (Different Probabilities, Same Rates)", "hyperexponential_pdf_samerate.svg");
distribution_plotter<boost::math::hyperexponential_distribution<> >
hyperexponential_plotter3;
{
const double probs1[] = {1.0};
const double rates1[] = {2.0};
hyperexponential_plotter3.add(boost::math::hyperexponential_distribution<>(probs1,rates1), "α=(1.0), λ=(2.0)");
const double probs2[] = {0.5,0.5};
const double rates2[] = {0.3,1.5};
hyperexponential_plotter3.add(boost::math::hyperexponential_distribution<>(probs2,rates2), "α=(0.5,0.5), λ=(0.3,1.5)");
const double probs3[] = {1.0/3.0,1.0/3.0,1.0/3.0};
const double rates3[] = {0.2,1.5,3.0};
hyperexponential_plotter3.add(boost::math::hyperexponential_distribution<>(probs2,rates2), "α=(1.0/3.0,1.0/3.0,1.0/3.0), λ=(0.2,1.5,3.0)");
}
hyperexponential_plotter3.plot("Hyperexponential Distribution PDF (Different Number of Phases, Same Mean)", "hyperexponential_pdf_samemean.svg");
*/
} // int main()
