1 /*! \file dist_graphs.cpp
2 \brief Produces Scalable Vector Graphic (.svg) files for all distributions.
3 \details These files can be viewed using most browsers,
4 though MS Internet Explorer requires a plugin from Adobe.
5 These file can be converted to .png using Inkscape
6 (see www.inkscape.org) Export Bit option which by default produces
7 a Portable Network Graphic file with that same filename but .png suffix instead of .svg.
8 Using Python, generate.sh does this conversion automatically for all .svg files in a folder.
9
10 \author John Maddock and Paul A. Bristow
11 */
12 // Copyright John Maddock 2008.
13 // Copyright Paul A. Bristow 2008, 2009, 2012, 2016
14 // Use, modification and distribution are subject to the
15 // Boost Software License, Version 1.0. (See accompanying file
16 // LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
17
18 #ifdef _MSC_VER
19 # pragma warning (disable : 4180) // qualifier applied to function type has no meaning; ignored
20 # pragma warning (disable : 4503) // decorated name length exceeded, name was truncated
21 # pragma warning (disable : 4512) // assignment operator could not be generated
22 # pragma warning (disable : 4224) // nonstandard extension used : formal parameter 'function_ptr' was previously defined as a type
23 # pragma warning (disable : 4127) // conditional expression is constant
24 #endif
25
26 #define BOOST_MATH_OVERFLOW_ERROR_POLICY ignore_error
27
28 #include <boost/math/distributions.hpp>
29 #include <boost/math/tools/roots.hpp>
30 #include <boost/svg_plot/svg_2d_plot.hpp>
31
32 #include <list>
33 #include <map>
34 #include <string>
35
36 template <class Dist>
37 struct is_discrete_distribution
38 : public boost::false_type{}; // Default is continuous distribution.
39
40 // Some discrete distributions.
41 template<class T, class P>
42 struct is_discrete_distribution<boost::math::bernoulli_distribution<T,P> >
43 : public boost::true_type{};
44 template<class T, class P>
45 struct is_discrete_distribution<boost::math::binomial_distribution<T,P> >
46 : public boost::true_type{};
47 template<class T, class P>
48 struct is_discrete_distribution<boost::math::negative_binomial_distribution<T,P> >
49 : public boost::true_type{};
50 template<class T, class P>
51 struct is_discrete_distribution<boost::math::poisson_distribution<T,P> >
52 : public boost::true_type{};
53 template<class T, class P>
54 struct is_discrete_distribution<boost::math::hypergeometric_distribution<T,P> >
55 : public boost::true_type{};
56
57
58 template <class Dist>
59 struct value_finder
60 {
value_findervalue_finder61 value_finder(Dist const& d, typename Dist::value_type v)
62 : m_dist(d), m_value(v) {}
63
operator ()value_finder64 inline typename Dist::value_type operator()(const typename Dist::value_type& x)
65 {
66 return pdf(m_dist, x) - m_value;
67 }
68
69 private:
70 Dist m_dist;
71 typename Dist::value_type m_value;
72 }; // value_finder
73
74 template <class Dist>
75 class distribution_plotter
76 {
77 public:
distribution_plotter()78 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)79 distribution_plotter(bool pdf) : m_pdf(pdf), m_min_x(0), m_max_x(0), m_min_y(0), m_max_y(0) {}
80
add(const Dist & d,const std::string & name)81 void add(const Dist& d, const std::string& name)
82 {
83 // Add name of distribution to our list for later:
84 m_distributions.push_back(std::make_pair(name, d));
85 //
86 // Get the extent of the distribution from the support:
87 double a, b;
88 std::tr1::tie(a, b) = support(d);
89 //
90 // PDF maximum is at the mode (probably):
91 double mod;
92 try
93 {
94 mod = mode(d);
95 }
96 catch(const std::domain_error& )
97 { // but if not use the lower limit of support.
98 mod = a;
99 }
100 if((mod <= a) && !is_discrete_distribution<Dist>::value)
101 { // Continuous distribution at or below lower limit of support.
102 double margin = 1e-2; // Margin of 1% (say) to get lowest off the 'end stop'.
103 if((a != 0) && (fabs(a) > margin))
104 {
105 mod = a * (1 + ((a > 0) ? margin : -margin));
106 }
107 else
108 { // Case of mod near zero?
109 mod = margin;
110 }
111 }
112 double peek_y = pdf(d, mod);
113 double min_y = peek_y / 20;
114 //
115 // If the extent is "infinite" then find out how large it
116 // has to be for the PDF to decay to min_y:
117 //
118 if(a <= -(std::numeric_limits<double>::max)())
119 {
120 boost::uintmax_t max_iter = 500;
121 double guess = mod;
122 if((pdf(d, 0) > min_y) || (guess == 0))
123 guess = -1e-3;
124 a = boost::math::tools::bracket_and_solve_root(
125 value_finder<Dist>(d, min_y),
126 guess,
127 8.0,
128 true,
129 boost::math::tools::eps_tolerance<double>(10),
130 max_iter).first;
131 }
132 if(b >= (std::numeric_limits<double>::max)())
133 {
134 boost::uintmax_t max_iter = 500;
135 double guess = mod;
136 if(a <= 0)
137 if((pdf(d, 0) > min_y) || (guess == 0))
138 guess = 1e-3;
139 b = boost::math::tools::bracket_and_solve_root(
140 value_finder<Dist>(d, min_y),
141 guess,
142 8.0,
143 false,
144 boost::math::tools::eps_tolerance<double>(10),
145 max_iter).first;
146 }
147 //
148 // Recalculate peek_y and location of mod so that
149 // it's not too close to one end of the graph:
150 // otherwise we may be shooting off to infinity.
151 //
152 if(!is_discrete_distribution<Dist>::value)
153 {
154 if(mod <= a + (b-a)/50)
155 {
156 mod = a + (b-a)/50;
157 }
158 if(mod >= b - (b-a)/50)
159 {
160 mod = b - (b-a)/50;
161 }
162 peek_y = pdf(d, mod);
163 }
164 //
165 // Now set our limits:
166 //
167 if(peek_y > m_max_y)
168 m_max_y = peek_y;
169 if(m_max_x == m_min_x)
170 {
171 m_max_x = b;
172 m_min_x = a;
173 }
174 else
175 {
176 if(a < m_min_x)
177 m_min_x = a;
178 if(b > m_max_x)
179 m_max_x = b;
180 }
181 } // add
182
plot(const std::string & title,const std::string & file)183 void plot(const std::string& title, const std::string& file)
184 {
185 using namespace boost::svg;
186
187 static const svg_color colors[5] =
188 {
189 darkblue,
190 darkred,
191 darkgreen,
192 darkorange,
193 chartreuse
194 };
195
196 if(m_pdf == false)
197 {
198 m_min_y = 0;
199 m_max_y = 1;
200 }
201
202 std::cout << "Plotting " << title << " to " << file << std::endl;
203
204 svg_2d_plot plot;
205 plot.image_x_size(750);
206 plot.image_y_size(400);
207 plot.copyright_holder("John Maddock").copyright_date("2008").boost_license_on(true);
208 plot.coord_precision(4); // Avoids any visible steps.
209 plot.title_font_size(20);
210 plot.legend_title_font_size(15);
211 plot.title(title);
212 if((m_distributions.size() == 1) && (m_distributions.begin()->first == ""))
213 plot.legend_on(false);
214 else
215 plot.legend_on(true);
216 plot.title_on(true);
217 //plot.x_major_labels_on(true).y_major_labels_on(true);
218 //double x_delta = (m_max_x - m_min_x) / 10;
219 double y_delta = (m_max_y - m_min_y) / 10;
220 if(is_discrete_distribution<Dist>::value)
221 plot.x_range(m_min_x - 0.5, m_max_x + 0.5)
222 .y_range(m_min_y, m_max_y + y_delta);
223 else
224 plot.x_range(m_min_x, m_max_x)
225 .y_range(m_min_y, m_max_y + y_delta);
226 plot.x_label_on(true).x_label("Random Variable");
227 plot.y_label_on(true).y_label("Probability");
228 plot.plot_border_color(lightslategray)
229 .background_border_color(lightslategray)
230 .legend_border_color(lightslategray)
231 .legend_background_color(white);
232 //
233 // Work out axis tick intervals:
234 //
235 double l = std::floor(std::log10((m_max_x - m_min_x) / 10) + 0.5);
236 double interval = std::pow(10.0, (int)l);
237 if(((m_max_x - m_min_x) / interval) > 10)
238 interval *= 5;
239 if(is_discrete_distribution<Dist>::value)
240 {
241 interval = interval > 1 ? std::floor(interval) : 1;
242 plot.x_num_minor_ticks(0);
243 }
244 plot.x_major_interval(interval);
245 l = std::floor(std::log10((m_max_y - m_min_y) / 10) + 0.5);
246 interval = std::pow(10.0, (int)l);
247 if(((m_max_y - m_min_y) / interval) > 10)
248 interval *= 5;
249 plot.y_major_interval(interval);
250
251 int color_index = 0;
252
253 if(!is_discrete_distribution<Dist>::value)
254 {
255 // Continuous distribution:
256 for(std::list<std::pair<std::string, Dist> >::const_iterator i = m_distributions.begin();
257 i != m_distributions.end(); ++i)
258 {
259 double x = m_min_x;
260 double continuous_interval = (m_max_x - m_min_x) / 200;
261 std::map<double, double> data;
262 while(x <= m_max_x)
263 {
264 data[x] = m_pdf ? pdf(i->second, x) : cdf(i->second, x);
265 x += continuous_interval;
266 }
267 plot.plot(data, i->first)
268 .line_on(true)
269 .line_color(colors[color_index])
270 .line_width(1.)
271 .shape(none);
272
273 //.bezier_on(true) // Bezier can't cope with badly behaved like uniform & triangular.
274 ++color_index;
275 color_index = color_index % (sizeof(colors)/sizeof(colors[0]));
276 }
277 }
278 else
279 {
280 // Discrete distribution:
281 double x_width = 0.75 / m_distributions.size();
282 double x_off = -0.5 * 0.75;
283 for(std::list<std::pair<std::string, Dist> >::const_iterator i = m_distributions.begin();
284 i != m_distributions.end(); ++i)
285 {
286 double x = ceil(m_min_x);
287 double discrete_interval = 1;
288 std::map<double, double> data;
289 while(x <= m_max_x)
290 {
291 double p;
292 try{
293 p = m_pdf ? pdf(i->second, x) : cdf(i->second, x);
294 }
295 catch(const std::domain_error&)
296 {
297 p = 0;
298 }
299 data[x + x_off] = 0;
300 data[x + x_off + 0.00001] = p;
301 data[x + x_off + x_width] = p;
302 data[x + x_off + x_width + 0.00001] = 0;
303 x += discrete_interval;
304 }
305 x_off += x_width;
306 svg_2d_plot_series& s = plot.plot(data, i->first);
307 s.line_on(true)
308 .line_color(colors[color_index])
309 .line_width(1.)
310 .shape(none)
311 .area_fill(colors[color_index]);
312 ++color_index;
313 color_index = color_index % (sizeof(colors)/sizeof(colors[0]));
314 }
315 } // discrete
316 plot.write(file);
317 } // void plot(const std::string& title, const std::string& file)
318
319 private:
320 bool m_pdf;
321 std::list<std::pair<std::string, Dist> > m_distributions;
322 double m_min_x, m_max_x, m_min_y, m_max_y;
323 };
324
main()325 int main()
326 {
327 try
328 {
329 std::cout << "Distribution Graphs" << std::endl;
330 distribution_plotter<boost::math::gamma_distribution<> >
331 gamma_plotter;
332 gamma_plotter.add(boost::math::gamma_distribution<>(0.75), "shape = 0.75");
333 gamma_plotter.add(boost::math::gamma_distribution<>(1), "shape = 1");
334 gamma_plotter.add(boost::math::gamma_distribution<>(3), "shape = 3");
335 gamma_plotter.plot("Gamma Distribution PDF With Scale = 1", "gamma1_pdf.svg");
336
337 distribution_plotter<boost::math::gamma_distribution<> >
338 gamma_plotter2;
339 gamma_plotter2.add(boost::math::gamma_distribution<>(2, 0.5), "scale = 0.5");
340 gamma_plotter2.add(boost::math::gamma_distribution<>(2, 1), "scale = 1");
341 gamma_plotter2.add(boost::math::gamma_distribution<>(2, 2), "scale = 2");
342 gamma_plotter2.plot("Gamma Distribution PDF With Shape = 2", "gamma2_pdf.svg");
343
344 distribution_plotter<boost::math::normal>
345 normal_plotter;
346 normal_plotter.add(boost::math::normal(0, 1), "μ = 0, σ = 1");
347 normal_plotter.add(boost::math::normal(0, 0.5), "μ = 0, σ = 0.5");
348 normal_plotter.add(boost::math::normal(0, 2), "μ = 0, σ = 2");
349 normal_plotter.add(boost::math::normal(-1, 1), "μ = -1, σ = 1");
350 normal_plotter.add(boost::math::normal(1, 1), "μ = 1, σ = 1");
351 normal_plotter.plot("Normal Distribution PDF", "normal_pdf.svg");
352
353 distribution_plotter<boost::math::laplace>
354 laplace_plotter;
355 laplace_plotter.add(boost::math::laplace(0, 1), "μ = 0, σ = 1");
356 laplace_plotter.add(boost::math::laplace(0, 0.5), "μ = 0, σ = 0.5");
357 laplace_plotter.add(boost::math::laplace(0, 2), "μ = 0, σ = 2");
358 laplace_plotter.add(boost::math::laplace(-1, 1), "μ = -1, σ = 1");
359 laplace_plotter.add(boost::math::laplace(1, 1), "μ = 1, σ = 1");
360 laplace_plotter.plot("Laplace Distribution PDF", "laplace_pdf.svg");
361
362 distribution_plotter<boost::math::non_central_chi_squared>
363 nc_cs_plotter;
364 nc_cs_plotter.add(boost::math::non_central_chi_squared(20, 0), "v=20, λ=0");
365 nc_cs_plotter.add(boost::math::non_central_chi_squared(20, 1), "v=20, λ=1");
366 nc_cs_plotter.add(boost::math::non_central_chi_squared(20, 5), "v=20, λ=5");
367 nc_cs_plotter.add(boost::math::non_central_chi_squared(20, 10), "v=20, λ=10");
368 nc_cs_plotter.add(boost::math::non_central_chi_squared(20, 20), "v=20, λ=20");
369 nc_cs_plotter.add(boost::math::non_central_chi_squared(20, 100), "v=20, λ=100");
370 nc_cs_plotter.plot("Non Central Chi Squared PDF", "nccs_pdf.svg");
371
372 distribution_plotter<boost::math::non_central_beta>
373 nc_beta_plotter;
374 nc_beta_plotter.add(boost::math::non_central_beta(10, 15, 0), "α=10, β=15, δ=0");
375 nc_beta_plotter.add(boost::math::non_central_beta(10, 15, 1), "α=10, β=15, δ=1");
376 nc_beta_plotter.add(boost::math::non_central_beta(10, 15, 5), "α=10, β=15, δ=5");
377 nc_beta_plotter.add(boost::math::non_central_beta(10, 15, 10), "α=10, β=15, δ=10");
378 nc_beta_plotter.add(boost::math::non_central_beta(10, 15, 40), "α=10, β=15, δ=40");
379 nc_beta_plotter.add(boost::math::non_central_beta(10, 15, 100), "α=10, β=15, δ=100");
380 nc_beta_plotter.plot("Non Central Beta PDF", "nc_beta_pdf.svg");
381
382 distribution_plotter<boost::math::non_central_f>
383 nc_f_plotter;
384 nc_f_plotter.add(boost::math::non_central_f(10, 20, 0), "v1=10, v2=20, λ=0");
385 nc_f_plotter.add(boost::math::non_central_f(10, 20, 1), "v1=10, v2=20, λ=1");
386 nc_f_plotter.add(boost::math::non_central_f(10, 20, 5), "v1=10, v2=20, λ=5");
387 nc_f_plotter.add(boost::math::non_central_f(10, 20, 10), "v1=10, v2=20, λ=10");
388 nc_f_plotter.add(boost::math::non_central_f(10, 20, 40), "v1=10, v2=20, λ=40");
389 nc_f_plotter.add(boost::math::non_central_f(10, 20, 100), "v1=10, v2=20, λ=100");
390 nc_f_plotter.plot("Non Central F PDF", "nc_f_pdf.svg");
391
392 distribution_plotter<boost::math::non_central_t>
393 nc_t_plotter;
394 nc_t_plotter.add(boost::math::non_central_t(10, -10), "v=10, δ=-10");
395 nc_t_plotter.add(boost::math::non_central_t(10, -5), "v=10, δ=-5");
396 nc_t_plotter.add(boost::math::non_central_t(10, 0), "v=10, δ=0");
397 nc_t_plotter.add(boost::math::non_central_t(10, 5), "v=10, δ=5");
398 nc_t_plotter.add(boost::math::non_central_t(10, 10), "v=10, δ=10");
399 nc_t_plotter.add(boost::math::non_central_t(std::numeric_limits<double>::infinity(), 15), "v=inf, δ=15");
400 nc_t_plotter.plot("Non Central T PDF", "nc_t_pdf.svg");
401
402 distribution_plotter<boost::math::non_central_t>
403 nc_t_CDF_plotter(false);
404 nc_t_CDF_plotter.add(boost::math::non_central_t(10, -10), "v=10, δ=-10");
405 nc_t_CDF_plotter.add(boost::math::non_central_t(10, -5), "v=10, δ=-5");
406 nc_t_CDF_plotter.add(boost::math::non_central_t(10, 0), "v=10, δ=0");
407 nc_t_CDF_plotter.add(boost::math::non_central_t(10, 5), "v=10, δ=5");
408 nc_t_CDF_plotter.add(boost::math::non_central_t(10, 10), "v=10, δ=10");
409 nc_t_CDF_plotter.add(boost::math::non_central_t(std::numeric_limits<double>::infinity(), 15), "v=inf, δ=15");
410 nc_t_CDF_plotter.plot("Non Central T CDF", "nc_t_cdf.svg");
411
412 distribution_plotter<boost::math::beta_distribution<> >
413 beta_plotter;
414 beta_plotter.add(boost::math::beta_distribution<>(0.5, 0.5), "alpha=0.5, beta=0.5");
415 beta_plotter.add(boost::math::beta_distribution<>(5, 1), "alpha=5, beta=1");
416 beta_plotter.add(boost::math::beta_distribution<>(1, 3), "alpha=1, beta=3");
417 beta_plotter.add(boost::math::beta_distribution<>(2, 2), "alpha=2, beta=2");
418 beta_plotter.add(boost::math::beta_distribution<>(2, 5), "alpha=2, beta=5");
419 beta_plotter.plot("Beta Distribution PDF", "beta_pdf.svg");
420
421 distribution_plotter<boost::math::cauchy_distribution<> >
422 cauchy_plotter;
423 cauchy_plotter.add(boost::math::cauchy_distribution<>(-5, 1), "location = -5");
424 cauchy_plotter.add(boost::math::cauchy_distribution<>(0, 1), "location = 0");
425 cauchy_plotter.add(boost::math::cauchy_distribution<>(5, 1), "location = 5");
426 cauchy_plotter.plot("Cauchy Distribution PDF (scale = 1)", "cauchy_pdf1.svg");
427
428 distribution_plotter<boost::math::cauchy_distribution<> >
429 cauchy_plotter2;
430 cauchy_plotter2.add(boost::math::cauchy_distribution<>(0, 0.5), "scale = 0.5");
431 cauchy_plotter2.add(boost::math::cauchy_distribution<>(0, 1), "scale = 1");
432 cauchy_plotter2.add(boost::math::cauchy_distribution<>(0, 2), "scale = 2");
433 cauchy_plotter2.plot("Cauchy Distribution PDF (location = 0)", "cauchy_pdf2.svg");
434
435 distribution_plotter<boost::math::chi_squared_distribution<> >
436 chi_squared_plotter;
437 //chi_squared_plotter.add(boost::math::chi_squared_distribution<>(1), "v=1");
438 chi_squared_plotter.add(boost::math::chi_squared_distribution<>(2), "v=2");
439 chi_squared_plotter.add(boost::math::chi_squared_distribution<>(5), "v=5");
440 chi_squared_plotter.add(boost::math::chi_squared_distribution<>(10), "v=10");
441 chi_squared_plotter.plot("Chi Squared Distribution PDF", "chi_squared_pdf.svg");
442
443 distribution_plotter<boost::math::exponential_distribution<> >
444 exponential_plotter;
445 exponential_plotter.add(boost::math::exponential_distribution<>(0.5), "λ=0.5");
446 exponential_plotter.add(boost::math::exponential_distribution<>(1), "λ=1");
447 exponential_plotter.add(boost::math::exponential_distribution<>(2), "λ=2");
448 exponential_plotter.plot("Exponential Distribution PDF", "exponential_pdf.svg");
449
450 distribution_plotter<boost::math::extreme_value_distribution<> >
451 extreme_value_plotter;
452 extreme_value_plotter.add(boost::math::extreme_value_distribution<>(-5), "location=-5");
453 extreme_value_plotter.add(boost::math::extreme_value_distribution<>(0), "location=0");
454 extreme_value_plotter.add(boost::math::extreme_value_distribution<>(5), "location=5");
455 extreme_value_plotter.plot("Extreme Value Distribution PDF (shape=1)", "extreme_value_pdf1.svg");
456
457 distribution_plotter<boost::math::extreme_value_distribution<> >
458 extreme_value_plotter2;
459 extreme_value_plotter2.add(boost::math::extreme_value_distribution<>(0, 0.5), "shape=0.5");
460 extreme_value_plotter2.add(boost::math::extreme_value_distribution<>(0, 1), "shape=1");
461 extreme_value_plotter2.add(boost::math::extreme_value_distribution<>(0, 2), "shape=2");
462 extreme_value_plotter2.plot("Extreme Value Distribution PDF (location=0)", "extreme_value_pdf2.svg");
463
464 distribution_plotter<boost::math::fisher_f_distribution<> >
465 fisher_f_plotter;
466 fisher_f_plotter.add(boost::math::fisher_f_distribution<>(4, 4), "n=4, m=4");
467 fisher_f_plotter.add(boost::math::fisher_f_distribution<>(10, 4), "n=10, m=4");
468 fisher_f_plotter.add(boost::math::fisher_f_distribution<>(10, 10), "n=10, m=10");
469 fisher_f_plotter.add(boost::math::fisher_f_distribution<>(4, 10), "n=4, m=10");
470 fisher_f_plotter.plot("F Distribution PDF", "fisher_f_pdf.svg");
471
472 distribution_plotter<boost::math::lognormal_distribution<> >
473 lognormal_plotter;
474 lognormal_plotter.add(boost::math::lognormal_distribution<>(-1), "location=-1");
475 lognormal_plotter.add(boost::math::lognormal_distribution<>(0), "location=0");
476 lognormal_plotter.add(boost::math::lognormal_distribution<>(1), "location=1");
477 lognormal_plotter.plot("Lognormal Distribution PDF (scale=1)", "lognormal_pdf1.svg");
478
479 distribution_plotter<boost::math::lognormal_distribution<> >
480 lognormal_plotter2;
481 lognormal_plotter2.add(boost::math::lognormal_distribution<>(0, 0.5), "scale=0.5");
482 lognormal_plotter2.add(boost::math::lognormal_distribution<>(0, 1), "scale=1");
483 lognormal_plotter2.add(boost::math::lognormal_distribution<>(0, 2), "scale=2");
484 lognormal_plotter2.plot("Lognormal Distribution PDF (location=0)", "lognormal_pdf2.svg");
485
486 distribution_plotter<boost::math::pareto_distribution<> >
487 pareto_plotter; // Rely on 2nd parameter shape = 1 default.
488 pareto_plotter.add(boost::math::pareto_distribution<>(1), "scale=1");
489 pareto_plotter.add(boost::math::pareto_distribution<>(2), "scale=2");
490 pareto_plotter.add(boost::math::pareto_distribution<>(3), "scale=3");
491 pareto_plotter.plot("Pareto Distribution PDF (shape=1)", "pareto_pdf1.svg");
492
493 distribution_plotter<boost::math::pareto_distribution<> >
494 pareto_plotter2;
495 pareto_plotter2.add(boost::math::pareto_distribution<>(1, 0.5), "shape=0.5");
496 pareto_plotter2.add(boost::math::pareto_distribution<>(1, 1), "shape=1");
497 pareto_plotter2.add(boost::math::pareto_distribution<>(1, 2), "shape=2");
498 pareto_plotter2.plot("Pareto Distribution PDF (scale=1)", "pareto_pdf2.svg");
499
500 distribution_plotter<boost::math::rayleigh_distribution<> >
501 rayleigh_plotter;
502 rayleigh_plotter.add(boost::math::rayleigh_distribution<>(0.5), "σ=0.5");
503 rayleigh_plotter.add(boost::math::rayleigh_distribution<>(1), "σ=1");
504 rayleigh_plotter.add(boost::math::rayleigh_distribution<>(2), "σ=2");
505 rayleigh_plotter.add(boost::math::rayleigh_distribution<>(4), "σ=4");
506 rayleigh_plotter.add(boost::math::rayleigh_distribution<>(10), "σ=10");
507 rayleigh_plotter.plot("Rayleigh Distribution PDF", "rayleigh_pdf.svg");
508
509 distribution_plotter<boost::math::rayleigh_distribution<> >
510 rayleigh_cdf_plotter(false);
511 rayleigh_cdf_plotter.add(boost::math::rayleigh_distribution<>(0.5), "σ=0.5");
512 rayleigh_cdf_plotter.add(boost::math::rayleigh_distribution<>(1), "σ=1");
513 rayleigh_cdf_plotter.add(boost::math::rayleigh_distribution<>(2), "σ=2");
514 rayleigh_cdf_plotter.add(boost::math::rayleigh_distribution<>(4), "σ=4");
515 rayleigh_cdf_plotter.add(boost::math::rayleigh_distribution<>(10), "σ=10");
516 rayleigh_cdf_plotter.plot("Rayleigh Distribution CDF", "rayleigh_cdf.svg");
517
518 distribution_plotter<boost::math::skew_normal_distribution<> >
519 skew_normal_plotter;
520 skew_normal_plotter.add(boost::math::skew_normal_distribution<>(0,1,0), "{0,1,0}");
521 skew_normal_plotter.add(boost::math::skew_normal_distribution<>(0,1,1), "{0,1,1}");
522 skew_normal_plotter.add(boost::math::skew_normal_distribution<>(0,1,4), "{0,1,4}");
523 skew_normal_plotter.add(boost::math::skew_normal_distribution<>(0,1,20), "{0,1,20}");
524 skew_normal_plotter.add(boost::math::skew_normal_distribution<>(0,1,-2), "{0,1,-2}");
525 skew_normal_plotter.add(boost::math::skew_normal_distribution<>(-2,0.5,-1), "{-2,0.5,-1}");
526 skew_normal_plotter.plot("Skew Normal Distribution PDF", "skew_normal_pdf.svg");
527
528 distribution_plotter<boost::math::skew_normal_distribution<> >
529 skew_normal_cdf_plotter(false);
530 skew_normal_cdf_plotter.add(boost::math::skew_normal_distribution<>(0,1,0), "{0,1,0}");
531 skew_normal_cdf_plotter.add(boost::math::skew_normal_distribution<>(0,1,1), "{0,1,1}");
532 skew_normal_cdf_plotter.add(boost::math::skew_normal_distribution<>(0,1,4), "{0,1,4}");
533 skew_normal_cdf_plotter.add(boost::math::skew_normal_distribution<>(0,1,20), "{0,1,20}");
534 skew_normal_cdf_plotter.add(boost::math::skew_normal_distribution<>(0,1,-2), "{0,1,-2}");
535 skew_normal_cdf_plotter.add(boost::math::skew_normal_distribution<>(-2,0.5,-1), "{-2,0.5,-1}");
536 skew_normal_cdf_plotter.plot("Skew Normal Distribution CDF", "skew_normal_cdf.svg");
537
538 distribution_plotter<boost::math::triangular_distribution<> >
539 triangular_plotter;
540 triangular_plotter.add(boost::math::triangular_distribution<>(-1,0,1), "{-1,0,1}");
541 triangular_plotter.add(boost::math::triangular_distribution<>(0,1,1), "{0,1,1}");
542 triangular_plotter.add(boost::math::triangular_distribution<>(0,1,3), "{0,1,3}");
543 triangular_plotter.add(boost::math::triangular_distribution<>(0,0.5,1), "{0,0.5,1}");
544 triangular_plotter.add(boost::math::triangular_distribution<>(-2,0,3), "{-2,0,3}");
545 triangular_plotter.plot("Triangular Distribution PDF", "triangular_pdf.svg");
546
547 distribution_plotter<boost::math::triangular_distribution<> >
548 triangular_cdf_plotter(false);
549 triangular_cdf_plotter.add(boost::math::triangular_distribution<>(-1,0,1), "{-1,0,1}");
550 triangular_cdf_plotter.add(boost::math::triangular_distribution<>(0,1,1), "{0,1,1}");
551 triangular_cdf_plotter.add(boost::math::triangular_distribution<>(0,1,3), "{0,1,3}");
552 triangular_cdf_plotter.add(boost::math::triangular_distribution<>(0,0.5,1), "{0,0.5,1}");
553 triangular_cdf_plotter.add(boost::math::triangular_distribution<>(-2,0,3), "{-2,0,3}");
554 triangular_cdf_plotter.plot("Triangular Distribution CDF", "triangular_cdf.svg");
555
556 distribution_plotter<boost::math::students_t_distribution<> >
557 students_t_plotter;
558 students_t_plotter.add(boost::math::students_t_distribution<>(1), "v=1");
559 students_t_plotter.add(boost::math::students_t_distribution<>(5), "v=5");
560 students_t_plotter.add(boost::math::students_t_distribution<>(30), "v=30");
561 students_t_plotter.plot("Students T Distribution PDF", "students_t_pdf.svg");
562
563 distribution_plotter<boost::math::weibull_distribution<> >
564 weibull_plotter;
565 weibull_plotter.add(boost::math::weibull_distribution<>(0.75), "shape=0.75");
566 weibull_plotter.add(boost::math::weibull_distribution<>(1), "shape=1");
567 weibull_plotter.add(boost::math::weibull_distribution<>(5), "shape=5");
568 weibull_plotter.add(boost::math::weibull_distribution<>(10), "shape=10");
569 weibull_plotter.plot("Weibull Distribution PDF (scale=1)", "weibull_pdf1.svg");
570
571 distribution_plotter<boost::math::weibull_distribution<> >
572 weibull_plotter2;
573 weibull_plotter2.add(boost::math::weibull_distribution<>(3, 0.5), "scale=0.5");
574 weibull_plotter2.add(boost::math::weibull_distribution<>(3, 1), "scale=1");
575 weibull_plotter2.add(boost::math::weibull_distribution<>(3, 2), "scale=2");
576 weibull_plotter2.plot("Weibull Distribution PDF (shape=3)", "weibull_pdf2.svg");
577
578 distribution_plotter<boost::math::uniform_distribution<> >
579 uniform_plotter;
580 uniform_plotter.add(boost::math::uniform_distribution<>(0, 1), "{0,1}");
581 uniform_plotter.add(boost::math::uniform_distribution<>(0, 3), "{0,3}");
582 uniform_plotter.add(boost::math::uniform_distribution<>(-2, 3), "{-2,3}");
583 uniform_plotter.add(boost::math::uniform_distribution<>(-1, 1), "{-1,1}");
584 uniform_plotter.plot("Uniform Distribution PDF", "uniform_pdf.svg");
585
586 distribution_plotter<boost::math::uniform_distribution<> >
587 uniform_cdf_plotter(false);
588 uniform_cdf_plotter.add(boost::math::uniform_distribution<>(0, 1), "{0,1}");
589 uniform_cdf_plotter.add(boost::math::uniform_distribution<>(0, 3), "{0,3}");
590 uniform_cdf_plotter.add(boost::math::uniform_distribution<>(-2, 3), "{-2,3}");
591 uniform_cdf_plotter.add(boost::math::uniform_distribution<>(-1, 1), "{-1,1}");
592 uniform_cdf_plotter.plot("Uniform Distribution CDF", "uniform_cdf.svg");
593
594 distribution_plotter<boost::math::bernoulli_distribution<> >
595 bernoulli_plotter;
596 bernoulli_plotter.add(boost::math::bernoulli_distribution<>(0.25), "p=0.25");
597 bernoulli_plotter.add(boost::math::bernoulli_distribution<>(0.5), "p=0.5");
598 bernoulli_plotter.add(boost::math::bernoulli_distribution<>(0.75), "p=0.75");
599 bernoulli_plotter.plot("Bernoulli Distribution PDF", "bernoulli_pdf.svg");
600
601 distribution_plotter<boost::math::bernoulli_distribution<> >
602 bernoulli_cdf_plotter(false);
603 bernoulli_cdf_plotter.add(boost::math::bernoulli_distribution<>(0.25), "p=0.25");
604 bernoulli_cdf_plotter.add(boost::math::bernoulli_distribution<>(0.5), "p=0.5");
605 bernoulli_cdf_plotter.add(boost::math::bernoulli_distribution<>(0.75), "p=0.75");
606 bernoulli_cdf_plotter.plot("Bernoulli Distribution CDF", "bernoulli_cdf.svg");
607
608 distribution_plotter<boost::math::binomial_distribution<> >
609 binomial_plotter;
610 binomial_plotter.add(boost::math::binomial_distribution<>(5, 0.5), "n=5 p=0.5");
611 binomial_plotter.add(boost::math::binomial_distribution<>(20, 0.5), "n=20 p=0.5");
612 binomial_plotter.add(boost::math::binomial_distribution<>(50, 0.5), "n=50 p=0.5");
613 binomial_plotter.plot("Binomial Distribution PDF", "binomial_pdf_1.svg");
614
615 distribution_plotter<boost::math::binomial_distribution<> >
616 binomial_plotter2;
617 binomial_plotter2.add(boost::math::binomial_distribution<>(20, 0.1), "n=20 p=0.1");
618 binomial_plotter2.add(boost::math::binomial_distribution<>(20, 0.5), "n=20 p=0.5");
619 binomial_plotter2.add(boost::math::binomial_distribution<>(20, 0.9), "n=20 p=0.9");
620 binomial_plotter2.plot("Binomial Distribution PDF", "binomial_pdf_2.svg");
621
622 distribution_plotter<boost::math::negative_binomial_distribution<> >
623 negative_binomial_plotter;
624 negative_binomial_plotter.add(boost::math::negative_binomial_distribution<>(20, 0.25), "n=20 p=0.25");
625 negative_binomial_plotter.add(boost::math::negative_binomial_distribution<>(20, 0.5), "n=20 p=0.5");
626 negative_binomial_plotter.add(boost::math::negative_binomial_distribution<>(20, 0.75), "n=20 p=0.75");
627 negative_binomial_plotter.plot("Negative Binomial Distribution PDF", "negative_binomial_pdf_1.svg");
628
629 distribution_plotter<boost::math::negative_binomial_distribution<> >
630 negative_binomial_plotter2;
631 negative_binomial_plotter2.add(boost::math::negative_binomial_distribution<>(10, 0.5), "n=10 p=0.5");
632 negative_binomial_plotter2.add(boost::math::negative_binomial_distribution<>(20, 0.5), "n=20 p=0.5");
633 negative_binomial_plotter2.add(boost::math::negative_binomial_distribution<>(70, 0.5), "n=70 p=0.5");
634 negative_binomial_plotter2.plot("Negative Binomial Distribution PDF", "negative_binomial_pdf_2.svg");
635
636 distribution_plotter<boost::math::poisson_distribution<> >
637 poisson_plotter;
638 poisson_plotter.add(boost::math::poisson_distribution<>(5), "λ=5");
639 poisson_plotter.add(boost::math::poisson_distribution<>(10), "λ=10");
640 poisson_plotter.add(boost::math::poisson_distribution<>(20), "λ=20");
641 poisson_plotter.plot("Poisson Distribution PDF", "poisson_pdf_1.svg");
642
643 distribution_plotter<boost::math::hypergeometric_distribution<> >
644 hypergeometric_plotter;
645 hypergeometric_plotter.add(boost::math::hypergeometric_distribution<>(30, 50, 500), "N=500, r=50, n=30");
646 hypergeometric_plotter.add(boost::math::hypergeometric_distribution<>(30, 100, 500), "N=500, r=100, n=30");
647 hypergeometric_plotter.add(boost::math::hypergeometric_distribution<>(30, 250, 500), "N=500, r=250, n=30");
648 hypergeometric_plotter.add(boost::math::hypergeometric_distribution<>(30, 400, 500), "N=500, r=400, n=30");
649 hypergeometric_plotter.add(boost::math::hypergeometric_distribution<>(30, 450, 500), "N=500, r=450, n=30");
650 hypergeometric_plotter.plot("Hypergeometric Distribution PDF", "hypergeometric_pdf_1.svg");
651
652 distribution_plotter<boost::math::hypergeometric_distribution<> >
653 hypergeometric_plotter2;
654 hypergeometric_plotter2.add(boost::math::hypergeometric_distribution<>(50, 50, 500), "N=500, r=50, n=50");
655 hypergeometric_plotter2.add(boost::math::hypergeometric_distribution<>(100, 50, 500), "N=500, r=50, n=100");
656 hypergeometric_plotter2.add(boost::math::hypergeometric_distribution<>(250, 50, 500), "N=500, r=50, n=250");
657 hypergeometric_plotter2.add(boost::math::hypergeometric_distribution<>(400, 50, 500), "N=500, r=50, n=400");
658 hypergeometric_plotter2.add(boost::math::hypergeometric_distribution<>(450, 50, 500), "N=500, r=50, n=450");
659 hypergeometric_plotter2.plot("Hypergeometric Distribution PDF", "hypergeometric_pdf_2.svg");
660
661 }
662 catch (std::exception ex)
663 {
664 std::cout << ex.what() << std::endl;
665 }
666
667
668
669 /* these graphs for hyperexponential distribution not used.
670
671 distribution_plotter<boost::math::hyperexponential_distribution<> >
672 hyperexponential_plotter;
673 {
674 const double probs1_1[] = {1.0};
675 const double rates1_1[] = {1.0};
676 hyperexponential_plotter.add(boost::math::hyperexponential_distribution<>(probs1_1,rates1_1), "α=(1.0), λ=(1.0)");
677 const double probs2_1[] = {0.1,0.9};
678 const double rates2_1[] = {0.5,1.5};
679 hyperexponential_plotter.add(boost::math::hyperexponential_distribution<>(probs2_1,rates2_1), "α=(0.1,0.9), λ=(0.5,1.5)");
680 const double probs2_2[] = {0.9,0.1};
681 const double rates2_2[] = {0.5,1.5};
682 hyperexponential_plotter.add(boost::math::hyperexponential_distribution<>(probs2_2,rates2_2), "α=(0.9,0.1), λ=(0.5,1.5)");
683 const double probs3_1[] = {0.2,0.3,0.5};
684 const double rates3_1[] = {0.5,1.0,1.5};
685 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)");
686 const double probs3_2[] = {0.5,0.3,0.2};
687 const double rates3_2[] = {0.5,1.0,1.5};
688 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)");
689 }
690 hyperexponential_plotter.plot("Hyperexponential Distribution PDF", "hyperexponential_pdf.svg");
691
692 distribution_plotter<boost::math::hyperexponential_distribution<> >
693 hyperexponential_plotter2;
694 {
695 const double rates[] = {0.5,1.5};
696 const double probs1[] = {0.1,0.9};
697 hyperexponential_plotter2.add(boost::math::hyperexponential_distribution<>(probs1,rates), "α=(0.1,0.9), λ=(0.5,1.5)");
698 const double probs2[] = {0.6,0.4};
699 hyperexponential_plotter2.add(boost::math::hyperexponential_distribution<>(probs2,rates), "α=(0.6,0.4), λ=(0.5,1.5)");
700 const double probs3[] = {0.9,0.1};
701 hyperexponential_plotter2.add(boost::math::hyperexponential_distribution<>(probs3,rates), "α=(0.9,0.1), λ=(0.5,1.5)");
702 }
703 hyperexponential_plotter2.plot("Hyperexponential Distribution PDF (Different Probabilities, Same Rates)", "hyperexponential_pdf_samerate.svg");
704
705 distribution_plotter<boost::math::hyperexponential_distribution<> >
706 hyperexponential_plotter3;
707 {
708 const double probs1[] = {1.0};
709 const double rates1[] = {2.0};
710 hyperexponential_plotter3.add(boost::math::hyperexponential_distribution<>(probs1,rates1), "α=(1.0), λ=(2.0)");
711 const double probs2[] = {0.5,0.5};
712 const double rates2[] = {0.3,1.5};
713 hyperexponential_plotter3.add(boost::math::hyperexponential_distribution<>(probs2,rates2), "α=(0.5,0.5), λ=(0.3,1.5)");
714 const double probs3[] = {1.0/3.0,1.0/3.0,1.0/3.0};
715 const double rates3[] = {0.2,1.5,3.0};
716 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)");
717 }
718 hyperexponential_plotter3.plot("Hyperexponential Distribution PDF (Different Number of Phases, Same Mean)", "hyperexponential_pdf_samemean.svg");
719 */
720
721 } // int main()
722