Added user guide sections for complex numbers and distributions.
git-svn-id: https://svn.apache.org/repos/asf/jakarta/commons/proper/math/trunk@141198 13f79535-47bb-0310-9956-ffa450edef68
This commit is contained in:
Brent Worden
parent
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commit
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<item name="Numerical Analysis" href="/userguide/analysis.html"/>
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<item name="Special Functions" href="/userguide/special.html"/>
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<item name="Utilities" href="/userguide/utilities.html"/>
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<item name="Complex Numbers" href="/userguide/complex.html"/>
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<item name="Distributions" href="/userguide/distribution.html"/>
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</menu>
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&common-menus;
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@ -0,0 +1,84 @@
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<?xml version="1.0"?>
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<!--
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Copyright 2003-2004 The Apache Software Foundation
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Licensed under the Apache License, Version 2.0 (the "License");
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you may not use this file except in compliance with the License.
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You may obtain a copy of the License at
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http://www.apache.org/licenses/LICENSE-2.0
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Unless required by applicable law or agreed to in writing, software
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distributed under the License is distributed on an "AS IS" BASIS,
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WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
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See the License for the specific language governing permissions and
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limitations under the License.
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-->
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<?xml-stylesheet type="text/xsl" href="./xdoc.xsl"?>
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<!-- $Revision: 1.1 $ $Date: 2004/04/26 20:06:50 $ -->
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<document url="stat.html">
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<properties>
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<title>The Commons Math User Guide - Statistics</title>
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</properties>
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<body>
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<section name="7 Complex Numbers">
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<subsection name="7.1 Overview" href="overview">
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<p>
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The complex packages provides a complex number type as well as complex
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versions of common transcendental functions and complex number
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formatting.
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</p>
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</subsection>
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<subsection name="7.2 Complex Numbers" href="complex">
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<p>
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<a href="../apidocs/org/apache/commons/math/complex/Complex.html">
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org.apache.commons.math.complex.Complex</a> provides a complex number
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type that forms the basis for the complex functionality found in
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commons-math.
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</p>
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<p>
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To create a complex number, simply call the constructor passing in two
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floating-point arguments, the first being the real part of the
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complex number and the second being the imaginary part:
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<source>Complex c = new Complex(1.0, 3.0); // 1 + 3i</source>
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</p>
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<p>
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The <code>Complex</code> class provides many unary and binary
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complex number operations. These operations provide the means to add,
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subtract, multiple and, divide complex numbers along with other
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complex number functions similar to the real number functions found in
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<code>java.math.BigDecimal</code>:
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<source>Complex lhs = new Complex(1.0, 3.0);
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Complex rhs = new Complex(2.0, 5.0);
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Complex answer = lhs.add(rhs); // add two complex numbers
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answer = lhs.subtract(rhs); // subtract two complex numbers
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answer = lhs.abs(); // absolute value
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answer = lhs.conjugate(rhs); // complex conjugate</source>
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</p>
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</subsection>
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<subsection name="7.3 Complex Transcendental Functions" href="function">
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<p>
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<a href="../apidocs/org/apache/commons/math/complex/ComplexMath.html">
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org.apache.commons.math.complex.ComplexMath</a> provides
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implementations of serveral transcendental functions involving complex
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number arguments. These operations provide the means to compute the
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log, sine, tangent and, other complex values similar to the real
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number functions found in <code>java.lang.Math</code>:
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<source>Complex first = new Complex(1.0, 3.0);
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Complex second = new Complex(2.0, 5.0);
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Complex answer = ComplexMath.log(first); // natural logarithm.
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answer = ComplexMath.cos(first); // cosine
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answer = ComplexMath.pow(first, second); // first raised to the power of second</source>
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</p>
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</subsection>
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<subsection name="7.4 Complex Formatting" href="formatting">
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<p>This is yet to be written. Any contributions will be gratefully
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accepted!</p>
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</subsection>
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</section>
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</body>
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</document>
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@ -0,0 +1,94 @@
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<?xml version="1.0"?>
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<!--
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Copyright 2003-2004 The Apache Software Foundation
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Licensed under the Apache License, Version 2.0 (the "License");
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you may not use this file except in compliance with the License.
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You may obtain a copy of the License at
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http://www.apache.org/licenses/LICENSE-2.0
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Unless required by applicable law or agreed to in writing, software
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distributed under the License is distributed on an "AS IS" BASIS,
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WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
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See the License for the specific language governing permissions and
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limitations under the License.
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-->
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<?xml-stylesheet type="text/xsl" href="./xdoc.xsl"?>
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<!-- $Revision: 1.1 $ $Date: 2004/04/26 20:06:50 $ -->
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<document url="stat.html">
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<properties>
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<title>The Commons Math User Guide - Statistics</title>
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</properties>
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<body>
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<section name="8 Probability Distributions">
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<subsection name="8.1 Overview" href="overview">
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<p>
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The distributions package provide a framework for some commonly used
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probability distributions.
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</p>
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</subsection>
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<subsection name="8.2 Distribution Framework" href="distributions">
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<p>
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The distribution framework provides the means to compute probability density
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function (PDF) probabilities and cumulative distribution function (CDF)
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probabilities for common probability distributions. Along with the direct
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computation of PDF and CDF probabilities, the framework also allows for the
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computation of inverse PDF and inverse CDF values.
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</p>
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<p>
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In order to use the distribution framework, first a distribution object must
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be created. It is encouraged that all distribution object creation occurs via
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the <code>org.apache.commons.math.distribution.DistributionFactory</code>
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class. <code>DistributionFactory</code> is a simple factory used to create all
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of the distribution objects supported by Commons-Math. The typical usage of
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<code>DistributionFactory</code> to create a distribution object would be:
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</p>
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<source>DistributionFactory factory = DistributionFactory.newInstance();
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BinomialDistribution binomial = factory.createBinomialDistribution(10, .75);</source>
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<p>
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The distributions that can be instantiated via the <code>DistributionFactory</code>
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are detailed below:
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<table>
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<tr><th>Distribution</th><th>Factory Method</th><th>Parameters</th></tr>
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<tr><td>Binomial</td><td>createBinomialDistribution</td><td><div>Number of trials</div><div>Probability of success</div></td></tr>
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<tr><td>Chi-Squared</td><td>createChiSquaredDistribution</td><td><div>Degrees of freedom</div></td></tr>
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<tr><td>Exponential</td><td>createExponentialDistribution</td><td><div>Mean</div></td></tr>
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<tr><td>F</td><td>createFDistribution</td><td><div>Numerator degrees of freedom</div><div>Denominator degrees of freedom</div></td></tr>
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<tr><td>Gamma</td><td>createGammaDistribution</td><td><div>Alpha</div><div>Beta</div></td></tr>
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<tr><td>Hypergeometric</td><td>createHypogeometricDistribution</td><td><div>Population size</div><div>Number of successes in population</div><div>Sample size</div></td></tr>
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<tr><td>Normal (Gaussian)</td><td>createNormalDistribution</td><td><div>Mean</div><div>Standard Deviation</div></td></tr>
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<tr><td>t</td><td>createTDistribution</td><td><div>Degrees of freedom</div></td></tr>
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</table>
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</p>
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<p>
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Using a distribution object, PDF and CDF probabilities are easily computed
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using the <code>cumulativeProbability</code> methods. For a distribution <code>X</code>,
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and a domain value, <code>x</code>, <code>cumulativeProbability</code> computes
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<code>P(X <= x)</code> (i.e. the lower tail probability of <code>X</code>).
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</p>
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<source>DistributionFactory factory = DistributionFactory.newInstance();
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TDistribution t = factory.createBinomialDistribution(29);
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double lowerTail = t.cumulativeProbability(-2.656); // P(T <= -2.656)
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double upperTail = 1.0 - t.cumulativeProbability(2.75); // P(T >= 2.75)</source>
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<p>
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The inverse PDF and CDF values are just as easily computed using the
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<code>inverseCumulativeProbability</code>methods. For a distribution <code>X</code>,
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and a probability, <code>p</code>, <code>inverseCumulativeProbability</code>
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computes the domain value <code>x</code>, such that:
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<ul>
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<li><code>P(X <= x) = p</code>, for continuous distributions</li>
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<li><code>P(X <= x) <= p</code>, for discrete distributions</li>
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</ul>
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Notice the different cases for continuous and discrete distributions. This is the result
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of PDFs not being invertible functions. As such, for discrete distributions, an exact
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domain value can not be returned. Only the "best" domain value. For Commons-Math, the "best"
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domain value is determined by the largest domain value whose cumulative probability is
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less-than or equal to the given probability.
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</p>
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</subsection>
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</section>
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</body>
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</document>
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@ -17,7 +17,7 @@
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-->
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<?xml-stylesheet type="text/xsl" href="./xdoc.xsl"?>
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<!-- $Revision: 1.7 $ $Date: 2004/02/29 21:25:08 $ -->
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<!-- $Revision: 1.8 $ $Date: 2004/04/26 20:06:50 $ -->
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<document url="index.html">
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<properties>
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<title>The Commons Math User Guide - Table of Contents</title>
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@ -36,7 +36,7 @@
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<li><a href="overview.html#dependencies">0.5 Dependencies</a></li>
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</ul></li>
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<li><a href="stat.html">1. Statistics and Distributions</a>
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<li><a href="stat.html">1. Statistics</a>
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<ul>
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<li><a href="stat.html#overview">1.1 Overview</a></li>
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<li><a href="stat.html#univariate">1.2 Univariate statistics</a></li>
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@ -79,6 +79,18 @@
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<li><a href="utilities.html#math_utils">6.4 binomial coefficients, factorials and other common math functions</a></li>
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<li><a href="utilities.html#stat_utils">6.5 statistical computation utiliities</a></li>
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</ul></li>
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<li><a href="complex.html">7. Complex Numbers</a>
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<ul>
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<li><a href="complex.html#overview">7.1 Overview</a></li>
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<li><a href="complex.html#complex">7.2 Complex Numbers</a></li>
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<li><a href="complex.html#functions">7.3 Complex Transcendental Functions</a></li>
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<li><a href="complex.html#formatting">7.4 Complex Formatting</a></li>
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</ul></li>
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<li><a href="distribution.html">8. Probability Distributions</a>
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<ul>
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<li><a href="distribution.html#overview">8.1 Overview</a></li>
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<li><a href="distribution.html#distributions">8.2 Distribution Framework</a></li>
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</ul></li>
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</ul>
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</section>
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@ -17,7 +17,7 @@
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-->
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<?xml-stylesheet type="text/xsl" href="./xdoc.xsl"?>
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<!-- $Revision: 1.9 $ $Date: 2004/04/25 17:12:05 $ -->
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<!-- $Revision: 1.10 $ $Date: 2004/04/26 20:06:50 $ -->
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<document>
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<properties>
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<title>User Guide - Overview</title>
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@ -67,15 +67,18 @@
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<subsection name="0.3 How commons-math is organized" href="organization">
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<p>
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Commons Math is divided into 6 subpackages, based on functionality provided.
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<ol><li><a href="stat.html">org.apache.commons.math.stat</a> - statistics, statistical tests, probability distributions</li>
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<li><a href="analysis.html">org.apache.commons.math.analysis</a> - rootfinding and interpolation</li>
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<li><a href="random.html">org.apache.commons.math.random</a> - random numbers, strings and data generation</li>
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<li><a href="special.html">org.apache.commons.math.special</a> - special functions (Gamma, Beta) </li>
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<li><a href="linear.html">org.apache.commons.math.linear</a> - matrices, solving linear systems </li>
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<li><a href="utilities.html">org.apache.commons.math.util</a> - common math/stat functions extending java.lang.Math </li>
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</ol>
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Package javadocs are <a href="../apidocs/index.html">here</a>
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Commons Math is divided into eight subpackages, based on functionality provided.
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<ol>
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<li><a href="stat.html">org.apache.commons.math.stat</a> - statistics, statistical tests</li>
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<li><a href="analysis.html">org.apache.commons.math.analysis</a> - rootfinding and interpolation</li>
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<li><a href="random.html">org.apache.commons.math.random</a> - random numbers, strings and data generation</li>
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<li><a href="special.html">org.apache.commons.math.special</a> - special functions (Gamma, Beta) </li>
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<li><a href="linear.html">org.apache.commons.math.linear</a> - matrices, solving linear systems </li>
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<li><a href="utilities.html">org.apache.commons.math.util</a> - common math/stat functions extending java.lang.Math </li>
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<li><a href="complex.html">org.apache.commons.math.complex</a> - complex numbers</li>
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<li><a href="distribution.html">org.apache.commons.math.distribution</a> - probability distributions</li>
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</ol>
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Package javadocs are <a href="../apidocs/index.html">here</a>
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</p>
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</subsection>
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@ -17,7 +17,7 @@
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-->
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<?xml-stylesheet type="text/xsl" href="./xdoc.xsl"?>
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<!-- $Revision: 1.15 $ $Date: 2004/04/26 05:16:35 $ -->
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<!-- $Revision: 1.16 $ $Date: 2004/04/26 20:06:50 $ -->
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<document url="stat.html">
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<properties>
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<title>The Commons Math User Guide - Statistics</title>
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@ -345,66 +345,6 @@ System.out.println(regression.getSlopeStdErr()); // displays slope standard erro
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<p>This is yet to be written. Any contributions will be gratefully
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accepted!</p>
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</subsection>
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<subsection name="1.6 Distribution framework" href="distributions">
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<p>
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The distribution framework provides the means to compute probability density
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function (PDF) probabilities and cumulative distribution function (CDF)
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probabilities for common probability distributions. Along with the direct
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computation of PDF and CDF probabilities, the framework also allows for the
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computation of inverse PDF and inverse CDF values.
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</p>
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<p>
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In order to use the distribution framework, first a distribution object must
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be created. It is encouraged that all distribution object creation occurs via
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the <code>org.apache.commons.math.stat.distribution.DistributionFactory</code>
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class. <code>DistributionFactory</code> is a simple factory used to create all
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of the distribution objects supported by Commons-Math. The typical usage of
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<code>DistributionFactory</code> to create a distribution object would be:
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</p>
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<source>DistributionFactory factory = DistributionFactory.newInstance();
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BinomialDistribution binomial = factory.createBinomialDistribution(10, .75);</source>
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<p>
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The distributions that can be instantiated via the <code>DistributionFactory</code>
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are detailed below:
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<table>
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<tr><th>Distribution</th><th>Factory Method</th><th>Parameters</th></tr>
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<tr><td>Binomial</td><td>createBinomialDistribution</td><td><div>Number of trials</div><div>Probability of success</div></td></tr>
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<tr><td>Chi-Squared</td><td>createChiSquaredDistribution</td><td><div>Degrees of freedom</div></td></tr>
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<tr><td>Exponential</td><td>createExponentialDistribution</td><td><div>Mean</div></td></tr>
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<tr><td>F</td><td>createFDistribution</td><td><div>Numerator degrees of freedom</div><div>Denominator degrees of freedom</div></td></tr>
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<tr><td>Gamma</td><td>createGammaDistribution</td><td><div>Alpha</div><div>Beta</div></td></tr>
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<tr><td>Hypergeometric</td><td>createHypogeometricDistribution</td><td><div>Population size</div><div>Number of successes in population</div><div>Sample size</div></td></tr>
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<tr><td>Normal (Gaussian)</td><td>createNormalDistribution</td><td><div>Mean</div><div>Standard Deviation</div></td></tr>
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<tr><td>t</td><td>createTDistribution</td><td><div>Degrees of freedom</div></td></tr>
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</table>
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</p>
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<p>
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Using a distribution object, PDF and CDF probabilities are easily computed
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using the <code>cumulativeProbability</code> methods. For a distribution <code>X</code>,
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and a domain value, <code>x</code>, <code>cumulativeProbability</code> computes
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<code>P(X <= x)</code> (i.e. the lower tail probability of <code>X</code>).
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</p>
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<source>DistributionFactory factory = DistributionFactory.newInstance();
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TDistribution t = factory.createBinomialDistribution(29);
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double lowerTail = t.cumulativeProbability(-2.656); // P(T <= -2.656)
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double upperTail = 1.0 - t.cumulativeProbability(2.75); // P(T >= 2.75)</source>
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<p>
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The inverse PDF and CDF values are just as easily computed using the
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<code>inverseCumulativeProbability</code>methods. For a distribution <code>X</code>,
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and a probability, <code>p</code>, <code>inverseCumulativeProbability</code>
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computes the domain value <code>x</code>, such that:
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<ul>
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<li><code>P(X <= x) = p</code>, for continuous distributions</li>
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<li><code>P(X <= x) <= p</code>, for discrete distributions</li>
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</ul>
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Notice the different cases for continuous and discrete distributions. This is the result
|
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of PDFs not being invertible functions. As such, for discrete distributions, an exact
|
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domain value can not be returned. Only the "best" domain value. For Commons-Math, the "best"
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domain value is determined by the largest domain value whose cumulative probability is
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less-than or equal to the given probability.
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</p>
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</subsection>
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</section>
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</body>
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||||
</document>
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|
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