1<html> 2<head> 3<meta http-equiv="Content-Type" content="text/html; charset=UTF-8"> 4<title>Conceptual Requirements for Distribution Types</title> 5<link rel="stylesheet" href="../math.css" type="text/css"> 6<meta name="generator" content="DocBook XSL Stylesheets V1.79.1"> 7<link rel="home" href="../index.html" title="Math Toolkit 2.12.0"> 8<link rel="up" href="../using_udt.html" title="Chapter 20. Use with User-Defined Floating-Point Types - Boost.Multiprecision and others"> 9<link rel="prev" href="real_concepts.html" title="Conceptual Requirements for Real Number Types"> 10<link rel="next" href="archetypes.html" title="Conceptual Archetypes for Reals and Distributions"> 11</head> 12<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF"> 13<table cellpadding="2" width="100%"><tr> 14<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../../boost.png"></td> 15<td align="center"><a href="../../../../../index.html">Home</a></td> 16<td align="center"><a href="../../../../../libs/libraries.htm">Libraries</a></td> 17<td align="center"><a href="http://www.boost.org/users/people.html">People</a></td> 18<td align="center"><a href="http://www.boost.org/users/faq.html">FAQ</a></td> 19<td align="center"><a href="../../../../../more/index.htm">More</a></td> 20</tr></table> 21<hr> 22<div class="spirit-nav"> 23<a accesskey="p" href="real_concepts.html"><img src="../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../using_udt.html"><img src="../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../index.html"><img src="../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="archetypes.html"><img src="../../../../../doc/src/images/next.png" alt="Next"></a> 24</div> 25<div class="section"> 26<div class="titlepage"><div><div><h2 class="title" style="clear: both"> 27<a name="math_toolkit.dist_concept"></a><a class="link" href="dist_concept.html" title="Conceptual Requirements for Distribution Types">Conceptual Requirements for 28 Distribution Types</a> 29</h2></div></div></div> 30<p> 31 A <span class="emphasis"><em>DistributionType</em></span> is a type that implements the following 32 conceptual requirements, and encapsulates a statistical distribution. 33 </p> 34<p> 35 Please note that this documentation should not be used as a substitute for 36 the <a class="link" href="dist_ref.html" title="Statistical Distributions Reference">reference documentation</a>, and 37 <a class="link" href="stat_tut.html" title="Statistical Distributions Tutorial">tutorial</a> of the statistical distributions. 38 </p> 39<p> 40 In the following table, <span class="emphasis"><em>d</em></span> is an object of type <code class="computeroutput"><span class="identifier">DistributionType</span></code>, <span class="emphasis"><em>cd</em></span> 41 is an object of type <code class="computeroutput"><span class="keyword">const</span> <span class="identifier">DistributionType</span></code> 42 and <span class="emphasis"><em>cr</em></span> is an object of a type convertible to <code class="computeroutput"><span class="identifier">RealType</span></code>. 43 </p> 44<div class="informaltable"><table class="table"> 45<colgroup> 46<col> 47<col> 48<col> 49</colgroup> 50<thead><tr> 51<th> 52 <p> 53 Expression 54 </p> 55 </th> 56<th> 57 <p> 58 Result Type 59 </p> 60 </th> 61<th> 62 <p> 63 Notes 64 </p> 65 </th> 66</tr></thead> 67<tbody> 68<tr> 69<td> 70 <p> 71 DistributionType::value_type 72 </p> 73 </td> 74<td> 75 <p> 76 RealType 77 </p> 78 </td> 79<td> 80 <p> 81 The real-number type <span class="emphasis"><em>RealType</em></span> upon which the 82 distribution operates. 83 </p> 84 </td> 85</tr> 86<tr> 87<td> 88 <p> 89 DistributionType::policy_type 90 </p> 91 </td> 92<td> 93 <p> 94 RealType 95 </p> 96 </td> 97<td> 98 <p> 99 The <a class="link" href="../policy.html" title="Chapter 21. Policies: Controlling Precision, Error Handling etc">Policy</a> to use when evaluating functions 100 that depend on this distribution. 101 </p> 102 </td> 103</tr> 104<tr> 105<td> 106 <p> 107 d = cd 108 </p> 109 </td> 110<td> 111 <p> 112 Distribution& 113 </p> 114 </td> 115<td> 116 <p> 117 Distribution types are assignable. 118 </p> 119 </td> 120</tr> 121<tr> 122<td> 123 <p> 124 Distribution(cd) 125 </p> 126 </td> 127<td> 128 <p> 129 Distribution 130 </p> 131 </td> 132<td> 133 <p> 134 Distribution types are copy constructible. 135 </p> 136 </td> 137</tr> 138<tr> 139<td> 140 <p> 141 pdf(cd, cr) 142 </p> 143 </td> 144<td> 145 <p> 146 RealType 147 </p> 148 </td> 149<td> 150 <p> 151 Returns the PDF of the distribution. 152 </p> 153 </td> 154</tr> 155<tr> 156<td> 157 <p> 158 cdf(cd, cr) 159 </p> 160 </td> 161<td> 162 <p> 163 RealType 164 </p> 165 </td> 166<td> 167 <p> 168 Returns the CDF of the distribution. 169 </p> 170 </td> 171</tr> 172<tr> 173<td> 174 <p> 175 cdf(complement(cd, cr)) 176 </p> 177 </td> 178<td> 179 <p> 180 RealType 181 </p> 182 </td> 183<td> 184 <p> 185 Returns the complement of the CDF of the distribution, the same as: 186 <code class="computeroutput"><span class="number">1</span><span class="special">-</span><span class="identifier">cdf</span><span class="special">(</span><span class="identifier">cd</span><span class="special">,</span> <span class="identifier">cr</span><span class="special">)</span></code> 187 </p> 188 </td> 189</tr> 190<tr> 191<td> 192 <p> 193 quantile(cd, cr) 194 </p> 195 </td> 196<td> 197 <p> 198 RealType 199 </p> 200 </td> 201<td> 202 <p> 203 Returns the quantile (or percentile) of the distribution. 204 </p> 205 </td> 206</tr> 207<tr> 208<td> 209 <p> 210 quantile(complement(cd, cr)) 211 </p> 212 </td> 213<td> 214 <p> 215 RealType 216 </p> 217 </td> 218<td> 219 <p> 220 Returns the quantile (or percentile) of the distribution, starting 221 from the complement of the probability, the same as: <code class="computeroutput"><span class="identifier">quantile</span><span class="special">(</span><span class="identifier">cd</span><span class="special">,</span> <span class="number">1</span><span class="special">-</span><span class="identifier">cr</span><span class="special">)</span></code> 222 </p> 223 </td> 224</tr> 225<tr> 226<td> 227 <p> 228 chf(cd, cr) 229 </p> 230 </td> 231<td> 232 <p> 233 RealType 234 </p> 235 </td> 236<td> 237 <p> 238 Returns the cumulative hazard function of the distribution. 239 </p> 240 </td> 241</tr> 242<tr> 243<td> 244 <p> 245 hazard(cd, cr) 246 </p> 247 </td> 248<td> 249 <p> 250 RealType 251 </p> 252 </td> 253<td> 254 <p> 255 Returns the hazard function of the distribution. 256 </p> 257 </td> 258</tr> 259<tr> 260<td> 261 <p> 262 kurtosis(cd) 263 </p> 264 </td> 265<td> 266 <p> 267 RealType 268 </p> 269 </td> 270<td> 271 <p> 272 Returns the kurtosis of the distribution. 273 </p> 274 </td> 275</tr> 276<tr> 277<td> 278 <p> 279 kurtosis_excess(cd) 280 </p> 281 </td> 282<td> 283 <p> 284 RealType 285 </p> 286 </td> 287<td> 288 <p> 289 Returns the kurtosis excess of the distribution. 290 </p> 291 </td> 292</tr> 293<tr> 294<td> 295 <p> 296 mean(cd) 297 </p> 298 </td> 299<td> 300 <p> 301 RealType 302 </p> 303 </td> 304<td> 305 <p> 306 Returns the mean of the distribution. 307 </p> 308 </td> 309</tr> 310<tr> 311<td> 312 <p> 313 mode(cd) 314 </p> 315 </td> 316<td> 317 <p> 318 RealType 319 </p> 320 </td> 321<td> 322 <p> 323 Returns the mode of the distribution. 324 </p> 325 </td> 326</tr> 327<tr> 328<td> 329 <p> 330 skewness(cd) 331 </p> 332 </td> 333<td> 334 <p> 335 RealType 336 </p> 337 </td> 338<td> 339 <p> 340 Returns the skewness of the distribution. 341 </p> 342 </td> 343</tr> 344<tr> 345<td> 346 <p> 347 standard_deviation(cd) 348 </p> 349 </td> 350<td> 351 <p> 352 RealType 353 </p> 354 </td> 355<td> 356 <p> 357 Returns the standard deviation of the distribution. 358 </p> 359 </td> 360</tr> 361<tr> 362<td> 363 <p> 364 variance(cd) 365 </p> 366 </td> 367<td> 368 <p> 369 RealType 370 </p> 371 </td> 372<td> 373 <p> 374 Returns the variance of the distribution. 375 </p> 376 </td> 377</tr> 378</tbody> 379</table></div> 380</div> 381<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr> 382<td align="left"></td> 383<td align="right"><div class="copyright-footer">Copyright © 2006-2019 Nikhar 384 Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos, 385 Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan 386 Råde, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, 387 Daryle Walker and Xiaogang Zhang<p> 388 Distributed under the Boost Software License, Version 1.0. (See accompanying 389 file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>) 390 </p> 391</div></td> 392</tr></table> 393<hr> 394<div class="spirit-nav"> 395<a accesskey="p" href="real_concepts.html"><img src="../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../using_udt.html"><img src="../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../index.html"><img src="../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="archetypes.html"><img src="../../../../../doc/src/images/next.png" alt="Next"></a> 396</div> 397</body> 398</html> 399
