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29 </h2></div></div></div>
31 <dt><span class=
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32 <dt><span class=
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39 </h3></div></div></div>
43 <div class=
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"1">
52 <div class=
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152 </h3></div></div></div>
153 <div class=
"variablelist">
154 <p class=
"title"><b>A Variable List
</b></p>
156 <dt><span class=
"term">term
1</span></dt>
158 The definition of term
1
160 <dt><span class=
"term">term
2</span></dt>
162 The definition of term
2
164 <dt><span class=
"term">term
3</span></dt>
166 The definition of term
3
171 <div class=
"section">
172 <div class=
"titlepage"><div><div><h3 class=
"title">
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174 </h3></div></div></div>
176 Here's a big table with code and other tricky things:
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">
206 f(x;
α,
β) = x
<sup>α -
1</sup> (
1 - x)
<sup>β -
1</sup> / B(
α,
β)
209 Implemented using ibeta_derivative(a, b, x).
221 Using the incomplete beta function ibeta(a, b, x)
245 Using the inverse incomplete beta function ibeta_inv(a, b, p)
252 quantile from the complement
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>
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>
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>
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>
325 <span class=
"inlinemediaobject"><img src=
"../images/beta_dist_kurtosis.png" alt=
"beta_dist_kurtosis"></span>
337 <code class=
"computeroutput"><span class=
"identifier">kurtosis
</span> <span class=
"special">+
</span>
338 <span class=
"number">3</span></code>
357 from mean and variance
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>
376 from mean and variance
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>
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>
395 from cdf and probability x
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>
404 Implemented in terms of the inverse incomplete beta functions
407 ibeta_inva, and ibeta_invb respectively.
414 <code class=
"computeroutput"><span class=
"identifier">estimate_alpha
</span></code>
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>
428 <code class=
"computeroutput"><span class=
"identifier">estimate_beta
</span></code>
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>
442 <br class=
"table-break">
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
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>)
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