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  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&#160;20.&#160;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&amp;
 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 &#169; 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       R&#229;de, 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>)
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