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4<title>Conceptual Requirements for Distribution Types</title>
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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;15.&#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>
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383<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014 Nikhar Agrawal,
384 Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos, Hubert
385 Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam Sewani,
386 Benjamin Sobotta, Thijs van den Berg, Daryle Walker and Xiaogang Zhang<p>
387 Distributed under the Boost Software License, Version 1.0. (See accompanying
388 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>)
389 </p>
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