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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 | ||
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> |