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1<html> 2<head> 3<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII"> 4<title>Lists and Tables</title> 5<link rel="stylesheet" href="../../../../doc/src/boostbook.css" type="text/css"> 6<meta name="generator" content="DocBook XSL Stylesheets V1.75.2"> 7<link rel="home" href="../index.html" title="Document To Test Formatting"> 8<link rel="up" href="../index.html" title="Document To Test Formatting"> 9<link rel="prev" href="blurbs.html" title="Blurbs"> 10<link rel="next" href="images.html" title="Images"> 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="blurbs.html"><img src="../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../index.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="images.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="document_to_test_formatting.lists_and_tables"></a><a class="link" href="lists_and_tables.html" title="Lists and Tables">Lists and 28 Tables</a> 29</h2></div></div></div> 30<div class="toc"><dl> 31<dt><span class="section"><a href="lists_and_tables.html#document_to_test_formatting.lists_and_tables.lists">Lists</a></span></dt> 32<dt><span class="section"><a href="lists_and_tables.html#document_to_test_formatting.lists_and_tables.variable_lists">Variable 33 Lists</a></span></dt> 34<dt><span class="section"><a href="lists_and_tables.html#document_to_test_formatting.lists_and_tables.tables">Tables</a></span></dt> 35</dl></div> 36<div class="section"> 37<div class="titlepage"><div><div><h3 class="title"> 38<a name="document_to_test_formatting.lists_and_tables.lists"></a><a class="link" href="lists_and_tables.html#document_to_test_formatting.lists_and_tables.lists" title="Lists">Lists</a> 39</h3></div></div></div> 40<p> 41 A numbered list: 42 </p> 43<div class="orderedlist"><ol class="orderedlist" type="1"> 44<li class="listitem"> 45 One 46 </li> 47<li class="listitem"> 48 Two 49 </li> 50<li class="listitem"> 51 Three 52 <div class="orderedlist"><ol class="orderedlist" type="a"> 53<li class="listitem"> 54 Three.a 55 </li> 56<li class="listitem"> 57 Three.b 58 </li> 59<li class="listitem"> 60 Three.c 61 </li> 62</ol></div> 63 </li> 64<li class="listitem"> 65 Four 66 <div class="orderedlist"><ol class="orderedlist" type="a"><li class="listitem"> 67 Four.a 68 <div class="orderedlist"><ol class="orderedlist" type="i"> 69<li class="listitem"> 70 Four.a.i 71 </li> 72<li class="listitem"> 73 Four.a.ii 74 </li> 75</ol></div> 76 </li></ol></div> 77 </li> 78<li class="listitem"> 79 Five 80 </li> 81</ol></div> 82<p> 83 An unordered list: 84 </p> 85<div class="itemizedlist"><ul class="itemizedlist" type="disc"> 86<li class="listitem"> 87 First 88 </li> 89<li class="listitem"> 90 Second 91 </li> 92<li class="listitem"> 93 Third 94 </li> 95</ul></div> 96<p> 97 A mixture of the two: 98 </p> 99<div class="orderedlist"><ol class="orderedlist" type="1"> 100<li class="listitem"> 101 1 102 <div class="itemizedlist"><ul class="itemizedlist" type="disc"> 103<li class="listitem"> 104 1.a 105 <div class="orderedlist"><ol class="orderedlist" type="a"> 106<li class="listitem"> 107 1.a.1 108 </li> 109<li class="listitem"> 110 1.a.2 111 </li> 112</ol></div> 113 </li> 114<li class="listitem"> 115 1.b 116 </li> 117</ul></div> 118 </li> 119<li class="listitem"> 120 2 121 <div class="itemizedlist"><ul class="itemizedlist" type="disc"> 122<li class="listitem"> 123 2.a 124 </li> 125<li class="listitem"> 126 2.b 127 <div class="orderedlist"><ol class="orderedlist" type="a"> 128<li class="listitem"> 129 2.b.1 130 </li> 131<li class="listitem"> 132 2.b.2 133 <div class="itemizedlist"><ul class="itemizedlist" type="circle"> 134<li class="listitem"> 135 2.b.2.a 136 </li> 137<li class="listitem"> 138 2.b.2.b 139 </li> 140</ul></div> 141 </li> 142</ol></div> 143 </li> 144</ul></div> 145 </li> 146</ol></div> 147</div> 148<div class="section"> 149<div class="titlepage"><div><div><h3 class="title"> 150<a name="document_to_test_formatting.lists_and_tables.variable_lists"></a><a class="link" href="lists_and_tables.html#document_to_test_formatting.lists_and_tables.variable_lists" title="Variable Lists">Variable 151 Lists</a> 152</h3></div></div></div> 153<div class="variablelist"> 154<p class="title"><b>A Variable List</b></p> 155<dl> 156<dt><span class="term">term 1</span></dt> 157<dd><p> 158 The definition of term 1 159 </p></dd> 160<dt><span class="term">term 2</span></dt> 161<dd><p> 162 The definition of term 2 163 </p></dd> 164<dt><span class="term">term 3</span></dt> 165<dd><p> 166 The definition of term 3 167 </p></dd> 168</dl> 169</div> 170</div> 171<div class="section"> 172<div class="titlepage"><div><div><h3 class="title"> 173<a name="document_to_test_formatting.lists_and_tables.tables"></a><a class="link" href="lists_and_tables.html#document_to_test_formatting.lists_and_tables.tables" title="Tables">Tables</a> 174</h3></div></div></div> 175<p> 176 Here's a big table with code and other tricky things: 177 </p> 178<div class="table"> 179<a name="id769721"></a><p class="title"><b>Table 1. Notes on the Implementation of the Beta Distribution</b></p> 180<div class="table-contents"><table class="table" summary="Notes on the Implementation of the Beta Distribution"> 181<colgroup> 182<col> 183<col> 184</colgroup> 185<thead><tr> 186<th> 187 <p> 188 Function 189 </p> 190 </th> 191<th> 192 <p> 193 Implementation Notes 194 </p> 195 </th> 196</tr></thead> 197<tbody> 198<tr> 199<td> 200 <p> 201 pdf 202 </p> 203 </td> 204<td> 205 <p> 206 f(x;α,β) = x<sup>α - 1</sup> (1 - x)<sup>β -1</sup> / B(α, β) 207 </p> 208 <p> 209 Implemented using ibeta_derivative(a, b, x). 210 </p> 211 </td> 212</tr> 213<tr> 214<td> 215 <p> 216 cdf 217 </p> 218 </td> 219<td> 220 <p> 221 Using the incomplete beta function ibeta(a, b, x) 222 </p> 223 </td> 224</tr> 225<tr> 226<td> 227 <p> 228 cdf complement 229 </p> 230 </td> 231<td> 232 <p> 233 ibetac(a, b, x) 234 </p> 235 </td> 236</tr> 237<tr> 238<td> 239 <p> 240 quantile 241 </p> 242 </td> 243<td> 244 <p> 245 Using the inverse incomplete beta function ibeta_inv(a, b, p) 246 </p> 247 </td> 248</tr> 249<tr> 250<td> 251 <p> 252 quantile from the complement 253 </p> 254 </td> 255<td> 256 <p> 257 ibetac_inv(a, b, q) 258 </p> 259 </td> 260</tr> 261<tr> 262<td> 263 <p> 264 mean 265 </p> 266 </td> 267<td> 268 <p> 269 <code class="computeroutput"><span class="identifier">a</span><span class="special">/(</span><span class="identifier">a</span><span class="special">+</span><span class="identifier">b</span><span class="special">)</span></code> 270 </p> 271 </td> 272</tr> 273<tr> 274<td> 275 <p> 276 variance 277 </p> 278 </td> 279<td> 280 <p> 281 <code class="computeroutput"><span class="identifier">a</span> <span class="special">*</span> 282 <span class="identifier">b</span> <span class="special">/</span> 283 <span class="special">(</span><span class="identifier">a</span><span class="special">+</span><span class="identifier">b</span><span class="special">)^</span><span class="number">2</span> <span class="special">*</span> <span class="special">(</span><span class="identifier">a</span> <span class="special">+</span> 284 <span class="identifier">b</span> <span class="special">+</span> 285 <span class="number">1</span><span class="special">)</span></code> 286 </p> 287 </td> 288</tr> 289<tr> 290<td> 291 <p> 292 mode 293 </p> 294 </td> 295<td> 296 <p> 297 <code class="computeroutput"><span class="special">(</span><span class="identifier">a</span><span class="special">-</span><span class="number">1</span><span class="special">)</span> <span class="special">/</span> <span class="special">(</span><span class="identifier">a</span> 298 <span class="special">+</span> <span class="identifier">b</span> 299 <span class="special">+</span> <span class="number">2</span><span class="special">)</span></code> 300 </p> 301 </td> 302</tr> 303<tr> 304<td> 305 <p> 306 skewness 307 </p> 308 </td> 309<td> 310 <p> 311 <code class="computeroutput"><span class="number">2</span> <span class="special">(</span><span class="identifier">b</span><span class="special">-</span><span class="identifier">a</span><span class="special">)</span> 312 <span class="identifier">sqrt</span><span class="special">(</span><span class="identifier">a</span><span class="special">+</span><span class="identifier">b</span><span class="special">+</span><span class="number">1</span><span class="special">)/(</span><span class="identifier">a</span><span class="special">+</span><span class="identifier">b</span><span class="special">+</span><span class="number">2</span><span class="special">)</span> <span class="special">*</span> <span class="identifier">sqrt</span><span class="special">(</span><span class="identifier">a</span> 313 <span class="special">*</span> <span class="identifier">b</span><span class="special">)</span></code> 314 </p> 315 </td> 316</tr> 317<tr> 318<td> 319 <p> 320 kurtosis excess 321 </p> 322 </td> 323<td> 324 <p> 325 <span class="inlinemediaobject"><img src="../images/beta_dist_kurtosis.png" alt="beta_dist_kurtosis"></span> 326 </p> 327 </td> 328</tr> 329<tr> 330<td> 331 <p> 332 kurtosis 333 </p> 334 </td> 335<td> 336 <p> 337 <code class="computeroutput"><span class="identifier">kurtosis</span> <span class="special">+</span> 338 <span class="number">3</span></code> 339 </p> 340 </td> 341</tr> 342<tr> 343<td> 344 <p> 345 parameter estimation 346 </p> 347 </td> 348<td> 349 </td> 350</tr> 351<tr> 352<td> 353 <p> 354 alpha 355 </p> 356 <p> 357 from mean and variance 358 </p> 359 </td> 360<td> 361 <p> 362 <code class="computeroutput"><span class="identifier">mean</span> <span class="special">*</span> 363 <span class="special">((</span> <span class="special">(</span><span class="identifier">mean</span> <span class="special">*</span> 364 <span class="special">(</span><span class="number">1</span> 365 <span class="special">-</span> <span class="identifier">mean</span><span class="special">))</span> <span class="special">/</span> <span class="identifier">variance</span><span class="special">)-</span> 366 <span class="number">1</span><span class="special">)</span></code> 367 </p> 368 </td> 369</tr> 370<tr> 371<td> 372 <p> 373 beta 374 </p> 375 <p> 376 from mean and variance 377 </p> 378 </td> 379<td> 380 <p> 381 <code class="computeroutput"><span class="special">(</span><span class="number">1</span> 382 <span class="special">-</span> <span class="identifier">mean</span><span class="special">)</span> <span class="special">*</span> <span class="special">(((</span><span class="identifier">mean</span> 383 <span class="special">*</span> <span class="special">(</span><span class="number">1</span> <span class="special">-</span> <span class="identifier">mean</span><span class="special">))</span> 384 <span class="special">/</span><span class="identifier">variance</span><span class="special">)-</span><span class="number">1</span><span class="special">)</span></code> 385 </p> 386 </td> 387</tr> 388<tr> 389<td> 390 <p> 391 The member functions <code class="computeroutput"><span class="identifier">estimate_alpha</span></code> 392 and <code class="computeroutput"><span class="identifier">estimate_beta</span></code> 393 </p> 394 <p> 395 from cdf and probability x 396 </p> 397 <p> 398 and <span class="bold"><strong>either</strong></span> <code class="computeroutput"><span class="identifier">alpha</span></code> 399 or <code class="computeroutput"><span class="identifier">beta</span></code> 400 </p> 401 </td> 402<td> 403 <p> 404 Implemented in terms of the inverse incomplete beta functions 405 </p> 406 <p> 407 ibeta_inva, and ibeta_invb respectively. 408 </p> 409 </td> 410</tr> 411<tr> 412<td> 413 <p> 414 <code class="computeroutput"><span class="identifier">estimate_alpha</span></code> 415 </p> 416 </td> 417<td> 418 <p> 419 <code class="computeroutput"><span class="identifier">ibeta_inva</span><span class="special">(</span><span class="identifier">beta</span><span class="special">,</span> 420 <span class="identifier">x</span><span class="special">,</span> 421 <span class="identifier">probability</span><span class="special">)</span></code> 422 </p> 423 </td> 424</tr> 425<tr> 426<td> 427 <p> 428 <code class="computeroutput"><span class="identifier">estimate_beta</span></code> 429 </p> 430 </td> 431<td> 432 <p> 433 <code class="computeroutput"><span class="identifier">ibeta_invb</span><span class="special">(</span><span class="identifier">alpha</span><span class="special">,</span> 434 <span class="identifier">x</span><span class="special">,</span> 435 <span class="identifier">probability</span><span class="special">)</span></code> 436 </p> 437 </td> 438</tr> 439</tbody> 440</table></div> 441</div> 442<br class="table-break"> 443</div> 444</div> 445<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr> 446<td align="left"></td> 447<td align="right"><div class="copyright-footer">Copyright © 2007 John Maddock, Joel de Guzman, Eric Niebler and Matias 448 Capeletto<p> 449 Distributed under the Boost Software License, Version 1.0. (See accompanying 450 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>) 451 </p> 452</div></td> 453</tr></table> 454<hr> 455<div class="spirit-nav"> 456<a accesskey="p" href="blurbs.html"><img src="../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../index.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="images.html"><img src="../../../../doc/src/images/next.png" alt="Next"></a> 457</div> 458</body> 459</html>