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commit d26f50b97bcfa25e896261d1363563ef32cbca7f
Author: Gilles Sadowski <gillese...@gmail.com>
AuthorDate: Wed Jun 9 16:41:11 2021 +0200
MATH-1603: Userguide update.
---
.../userguide/real_distribution_examples.png | Bin 180657 -> 0 bytes
src/site/xdoc/userguide/distribution.xml | 92 +++++----------------
src/site/xdoc/userguide/index.xml | 2 -
3 files changed, 19 insertions(+), 75 deletions(-)
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b/src/site/resources/images/userguide/real_distribution_examples.png
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diff --git a/src/site/xdoc/userguide/distribution.xml
b/src/site/xdoc/userguide/distribution.xml
index 6fa61f8..74a3e3d 100644
--- a/src/site/xdoc/userguide/distribution.xml
+++ b/src/site/xdoc/userguide/distribution.xml
@@ -16,7 +16,7 @@
See the License for the specific language governing permissions and
limitations under the License.
-->
-
+
<?xml-stylesheet type="text/xsl" href="./xdoc.xsl"?>
<document url="distribution.html">
<properties>
@@ -26,92 +26,38 @@
<section name="8 Probability Distributions">
<subsection name="8.1 Overview" href="overview">
<p>
- The distributions package provides a framework and implementations
for some commonly used
- probability distributions. Continuous univariate distributions are
represented by implementations of
- the <a
href="../apidocs/org/apache/commons/math4/distribution/RealDistribution.html">RealDistribution</a>
- interface. Discrete distributions implement
- <a
href="../apidocs/org/apache/commons/math4/distribution/IntegerDistribution.html">IntegerDistribution</a>
- (values must be mapped to integers) and there is an
- <a
href="../apidocs/org/apache/commons/math4/distribution/EnumeratedDistribution.html">EnumeratedDistribution</a>
- class representing discrete distributions with a finite, enumerated
set of values. Finally, multivariate
- real-valued distributions can be represented via the
- <a
href="../apidocs/org/apache/commons/math4/distribution/MultiVariateRealDistribution.html">MultivariateRealDistribution</a>
- interface.
- </p>
- <p>
- An overview of available continuous distributions:<br/>
- <img src="../images/userguide/real_distribution_examples.png"
alt="Overview of continuous distributions"/>
- </p>
- </subsection>
- <subsection name="8.2 Distribution Framework" href="distributions">
- <p>
- The distribution framework provides the means to compute probability
density
- functions (<code>density(·)</code>), probability mass
functions
- (<code>probability(·)</code>) and distribution functions
- (<code>cumulativeProbability(·)</code>) for both
- discrete (integer-valued) and continuous probability distributions.
- The framework also allows for the computation of inverse cumulative
probabilities
- and sampling from distributions.
+ Standard distributions are now available in the
+ <a
href="https://commons.apache.org/proper/commons-statistics/userguide/index.html";>
+ Commons Statistics</a> component.
</p>
<p>
- For an instance <code>f</code> of a distribution <code>F</code>,
- and a domain value, <code>x</code>,
<code>f.cumulativeProbability(x)</code>
- computes <code>P(X <= x)</code> where <code>X</code> is a random
variable distributed
- as <code>f</code>, i.e.,
<code>f.cumulativeProbability(·)</code> represents
- the distribution function of <code>f</code>. If <code>f</code> is
continuous,
- (implementing the <code>RealDistribution</code> interface) the
probability density
- function of <code>f</code> is represented by
<code>f.density(·)</code>.
- For discrete <code>f</code> (implementing
<code>IntegerDistribution</code>), the probability
- mass function is represented by
<code>f.probability(·)</code>. Continuous
- distributions also implement <code>probability(·)</code> with
the same
- definition (<code>f.probability(x)</code> represents <code>P(X =
x)</code>
- where <code>X</code> is distributed as <code>f</code>), though in
the continuous
- case, this will usually be identically 0.
- </p>
-<source>TDistribution t = new TDistribution(29);
-double lowerTail = t.cumulativeProbability(-2.656); // P(T(29) <=
-2.656)
-double upperTail = 1.0 - t.cumulativeProbability(2.75); // P(T(29) >=
2.75)</source>
- <p>
- All distributions implement a <code>sample()</code> method to
support random sampling from the
- distribution. Implementation classes expose constructors allowing
the default
- <a
href="../apidocs/org/apache/commons/math4/random/RandomGenerator.html">RandomGenerator</a>
- used by the sampling algorithm to be overridden. If sampling is not
going to be used, providing
- a null <code>RandomGenerator</code> constructor argument will avoid
the overhead of initializing
- the default generator.
+ Commons Math provides
+ <ul>
+ <li>
+ an <a
href="../apidocs/org/apache/commons/math4/legacy/distribution/EnumeratedDistribution.html">
+ EnumeratedDistribution</a> class that represents discrete
distributions of a finite,
+ enumerated set of values.
+ </li>
+ <li>
+ a <a
href="../apidocs/org/apache/commons/math4/legacy/distribution/MultiVariateNormalDistribution.html">
+ MultivariateNormalDistribution</a> interface that represents
multivariate Gaussian
+ distributions.
+ </li>
+ </ul>
</p>
<p>
Inverse distribution functions can be computed using the
<code>inverseCumulativeProbability</code> methods. For continuous
<code>f</code>
and <code>p</code> a probability,
<code>f.inverseCumulativeProbability(p)</code> returns
<code><ul>
- <li>inf{x in R | P(X≤x) ≥ p} for 0 < p < 1},</li>
- <li>inf{x in R | P(X≤x) > 0} for p = 0}.</li>
+ <li>inf{x in R | P(X≤x) ≥ p} for 0 < p < 1,</li>
+ <li>inf{x in R | P(X≤x) > 0} for p = 0.</li>
</ul></code> where <code>X</code> is distributed as
<code>f</code>.<br/>
For discrete <code>f</code>, the definition is the same, with
<code>Z</code> (the integers)
in place of <code>R</code>. Note that in the discrete case, the
≥ in the definition
can make a difference when <code>p</code> is an attained value of
the distribution.
</p>
</subsection>
- <!--
- TODO: add section on multivariate distributions
- -->
- <subsection name="8.3 User Defined Distributions" href="userdefined">
- <p>
- User-defined distributions can be implemented using
- <a
href="../apidocs/org/apache/commons/math4/distribution/RealDistribution.html">RealDistribution</a>,
- <a
href="../apidocs/org/apache/commons/math4/distribution/IntegerDistribution.html">IntegerDistribution</a>
and
- <a
href="../apidocs/org/apache/commons/math4/distribution/MultivariateRealDistribution.html">MultivariateRealDistribution</a>
- interfaces serve as base types. These serve as the basis for all the
distributions directly supported by
- Apache Commons Math. To aid in implementing distributions,
- the <a
href="../apidocs/org/apache/commons/math4/distribution/AbstractRealDistribution.html">AbstractRealDistribution</a>,
- <a
href="../apidocs/org/apache/commons/math4/distribution/AbstractIntegerDistribution.html">AbstractIntegerDistribution</a>
and
- <a
href="../apidocs/org/apache/commons/math4/distribution/AbstractMultivariateRealDistribution.html">AbstractMultivariateRealDistribution</a>
- provide implementation building blocks and offer basic distribution
functionality.
- By extending these abstract classes directly, much of the repetitive
distribution
- implementation is already developed and should save time and effort in
developing
- user-defined distributions.
- </p>
- </subsection>
</section>
</body>
</document>
diff --git a/src/site/xdoc/userguide/index.xml
b/src/site/xdoc/userguide/index.xml
index 81bdd22..2608aa8 100644
--- a/src/site/xdoc/userguide/index.xml
+++ b/src/site/xdoc/userguide/index.xml
@@ -103,8 +103,6 @@
<li><a href="distribution.html">8. Probability Distributions</a>
<ul>
<li><a href="distribution.html#a8.1_Overview">8.1
Overview</a></li>
- <li><a
href="distribution.html#a8.2_Distribution_Framework">8.2 Distribution
Framework</a></li>
- <li><a
href="distribution.html#a8.3_User_Defined_Distributions">8.3 User Defined
Distributions</a></li>
</ul></li>
<li><a href="fraction.html">9. Fractions</a>
<ul>
