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Distributions (Colt 1.2.0 - API Specification)
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cern.jet.random</FONT>
<BR>
Class Distributions</H2>
<PRE>
<A HREF="http://java.sun.com/j2se/1.4/docs/api/java/lang/Object.html" title="class or interface in java.lang">java.lang.Object</A>
<IMG SRC="../../../resources/inherit.gif" ALT="extended by"><B>cern.jet.random.Distributions</B>
</PRE>
<HR>
<DL>
<DT>public class <B>Distributions</B><DT>extends <A HREF="http://java.sun.com/j2se/1.4/docs/api/java/lang/Object.html" title="class or interface in java.lang">Object</A></DL>
<P>
Contains methods for conveniently generating pseudo-random numbers from special distributions such as the Burr, Cauchy, Erlang, Geometric, Lambda, Laplace, Logistic, Weibull, etc.
<p>
<b>About this class:</b>
<dt>All distributions are obtained by using a <b>uniform</b> pseudo-random number generator.
followed by a transformation to the desired distribution.
<p>
<b>Example usage:</b><pre>
cern.jet.random.engine.RandomEngine generator;
generator = new cern.jet.random.engine.MersenneTwister(new java.util.Date());
//generator = new edu.cornell.lassp.houle.RngPack.Ranecu(new java.util.Date());
//generator = new edu.cornell.lassp.houle.RngPack.Ranmar(new java.util.Date());
//generator = new edu.cornell.lassp.houle.RngPack.Ranlux(new java.util.Date());
//generator = AbstractDistribution.makeDefaultGenerator();
for (int i=1000000; --i >=0; ) {
int cauchy = Distributions.nextCauchy(generator);
...
}
</pre>
<P>
<P>
<DL>
<DT><B>Version:</B></DT>
<DD>1.0, 09/24/99</DD>
<DT><B>See Also:</B><DD><A HREF="../../../cern/jet/random/engine/MersenneTwister.html" title="class in cern.jet.random.engine"><CODE>MersenneTwister</CODE></A>,
<A HREF="http://java.sun.com/j2se/1.4/docs/api/java/util/Random.html" title="class or interface in java.util"><CODE>Random</CODE></A>,
<A HREF="http://java.sun.com/j2se/1.4/docs/api/java/lang/Math.html" title="class or interface in java.lang"><CODE>Math</CODE></A></DL>
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<CODE>static double</CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../cern/jet/random/Distributions.html#geometricPdf(int, double)">geometricPdf</A></B>(int k,
double p)</CODE>
<BR>
Returns the probability distribution function of the discrete geometric distribution.</TD>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
<CODE>static double</CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../cern/jet/random/Distributions.html#nextBurr1(double, int, cern.jet.random.engine.RandomEngine)">nextBurr1</A></B>(double r,
int nr,
<A HREF="../../../cern/jet/random/engine/RandomEngine.html" title="class in cern.jet.random.engine">RandomEngine</A> randomGenerator)</CODE>
<BR>
Returns a random number from the Burr II, VII, VIII, X Distributions.</TD>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
<CODE>static double</CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../cern/jet/random/Distributions.html#nextBurr2(double, double, int, cern.jet.random.engine.RandomEngine)">nextBurr2</A></B>(double r,
double k,
int nr,
<A HREF="../../../cern/jet/random/engine/RandomEngine.html" title="class in cern.jet.random.engine">RandomEngine</A> randomGenerator)</CODE>
<BR>
Returns a random number from the Burr III, IV, V, VI, IX, XII distributions.</TD>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
<CODE>static double</CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../cern/jet/random/Distributions.html#nextCauchy(cern.jet.random.engine.RandomEngine)">nextCauchy</A></B>(<A HREF="../../../cern/jet/random/engine/RandomEngine.html" title="class in cern.jet.random.engine">RandomEngine</A> randomGenerator)</CODE>
<BR>
Returns a cauchy distributed random number from the standard Cauchy distribution C(0,1).</TD>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
<CODE>static double</CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../cern/jet/random/Distributions.html#nextErlang(double, double, cern.jet.random.engine.RandomEngine)">nextErlang</A></B>(double variance,
double mean,
<A HREF="../../../cern/jet/random/engine/RandomEngine.html" title="class in cern.jet.random.engine">RandomEngine</A> randomGenerator)</CODE>
<BR>
Returns an erlang distributed random number with the given variance and mean.</TD>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
<CODE>static int</CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../cern/jet/random/Distributions.html#nextGeometric(double, cern.jet.random.engine.RandomEngine)">nextGeometric</A></B>(double p,
<A HREF="../../../cern/jet/random/engine/RandomEngine.html" title="class in cern.jet.random.engine">RandomEngine</A> randomGenerator)</CODE>
<BR>
Returns a discrete geometric distributed random number; <A HREF="http://www.statsoft.com/textbook/glosf.html#Geometric Distribution">Definition</A>.</TD>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
<CODE>static double</CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../cern/jet/random/Distributions.html#nextLambda(double, double, cern.jet.random.engine.RandomEngine)">nextLambda</A></B>(double l3,
double l4,
<A HREF="../../../cern/jet/random/engine/RandomEngine.html" title="class in cern.jet.random.engine">RandomEngine</A> randomGenerator)</CODE>
<BR>
Returns a lambda distributed random number with parameters l3 and l4.</TD>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
<CODE>static double</CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../cern/jet/random/Distributions.html#nextLaplace(cern.jet.random.engine.RandomEngine)">nextLaplace</A></B>(<A HREF="../../../cern/jet/random/engine/RandomEngine.html" title="class in cern.jet.random.engine">RandomEngine</A> randomGenerator)</CODE>
<BR>
Returns a Laplace (Double Exponential) distributed random number from the standard Laplace distribution L(0,1).</TD>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
<CODE>static double</CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../cern/jet/random/Distributions.html#nextLogistic(cern.jet.random.engine.RandomEngine)">nextLogistic</A></B>(<A HREF="../../../cern/jet/random/engine/RandomEngine.html" title="class in cern.jet.random.engine">RandomEngine</A> randomGenerator)</CODE>
<BR>
Returns a random number from the standard Logistic distribution Log(0,1).</TD>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
<CODE>static double</CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../cern/jet/random/Distributions.html#nextPowLaw(double, double, cern.jet.random.engine.RandomEngine)">nextPowLaw</A></B>(double alpha,
double cut,
<A HREF="../../../cern/jet/random/engine/RandomEngine.html" title="class in cern.jet.random.engine">RandomEngine</A> randomGenerator)</CODE>
<BR>
Returns a power-law distributed random number with the given exponent and lower cutoff.</TD>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
<CODE>static double</CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../cern/jet/random/Distributions.html#nextTriangular(cern.jet.random.engine.RandomEngine)">nextTriangular</A></B>(<A HREF="../../../cern/jet/random/engine/RandomEngine.html" title="class in cern.jet.random.engine">RandomEngine</A> randomGenerator)</CODE>
<BR>
Returns a random number from the standard Triangular distribution in (-1,1).</TD>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
<CODE>static double</CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../cern/jet/random/Distributions.html#nextWeibull(double, double, cern.jet.random.engine.RandomEngine)">nextWeibull</A></B>(double alpha,
double beta,
<A HREF="../../../cern/jet/random/engine/RandomEngine.html" title="class in cern.jet.random.engine">RandomEngine</A> randomGenerator)</CODE>
<BR>
Returns a weibull distributed random number.</TD>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
<CODE>static int</CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../cern/jet/random/Distributions.html#nextZipfInt(double, cern.jet.random.engine.RandomEngine)">nextZipfInt</A></B>(double z,
<A HREF="../../../cern/jet/random/engine/RandomEngine.html" title="class in cern.jet.random.engine">RandomEngine</A> randomGenerator)</CODE>
<BR>
Returns a zipfian distributed random number with the given skew.</TD>
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<TD><B>Methods inherited from class java.lang.<A HREF="http://java.sun.com/j2se/1.4/docs/api/java/lang/Object.html" title="class or interface in java.lang">Object</A></B></TD>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
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<A NAME="geometricPdf(int, double)"><!-- --></A><H3>
geometricPdf</H3>
<PRE>
public static double <B>geometricPdf</B>(int k,
double p)</PRE>
<DL>
<DD>Returns the probability distribution function of the discrete geometric distribution.
<p>
<tt>p(k) = p * (1-p)^k</tt> for <tt> k >= 0</tt>.
<p>
<P>
<DD><DL>
<DT><B>Parameters:</B><DD><CODE>k</CODE> - the argument to the probability distribution function.<DD><CODE>p</CODE> - the parameter of the probability distribution function.</DL>
</DD>
</DL>
<HR>
<A NAME="nextBurr1(double, int, cern.jet.random.engine.RandomEngine)"><!-- --></A><H3>
nextBurr1</H3>
<PRE>
public static double <B>nextBurr1</B>(double r,
int nr,
<A HREF="../../../cern/jet/random/engine/RandomEngine.html" title="class in cern.jet.random.engine">RandomEngine</A> randomGenerator)</PRE>
<DL>
<DD>Returns a random number from the Burr II, VII, VIII, X Distributions.
<p>
<b>Implementation:</b> Inversion method.
This is a port of <tt>burr1.c</tt> from the <A HREF="http://www.cis.tu-graz.ac.at/stat/stadl/random.html">C-RAND / WIN-RAND</A> library.
C-RAND's implementation, in turn, is based upon
<p>
L. Devroye (1986): Non-Uniform Random Variate Generation, Springer Verlag, New York.
<p>
<P>
<DD><DL>
<DT><B>Parameters:</B><DD><CODE>r</CODE> - must be > 0.<DD><CODE>nr</CODE> - the number of the burr distribution (e.g. 2,7,8,10).</DL>
</DD>
</DL>
<HR>
<A NAME="nextBurr2(double, double, int, cern.jet.random.engine.RandomEngine)"><!-- --></A><H3>
nextBurr2</H3>
<PRE>
public static double <B>nextBurr2</B>(double r,
double k,
int nr,
<A HREF="../../../cern/jet/random/engine/RandomEngine.html" title="class in cern.jet.random.engine">RandomEngine</A> randomGenerator)</PRE>
<DL>
<DD>Returns a random number from the Burr III, IV, V, VI, IX, XII distributions.
<p>
<b>Implementation:</b> Inversion method.
This is a port of <tt>burr2.c</tt> from the <A HREF="http://www.cis.tu-graz.ac.at/stat/stadl/random.html">C-RAND / WIN-RAND</A> library.
C-RAND's implementation, in turn, is based upon
<p>
L. Devroye (1986): Non-Uniform Random Variate Generation, Springer Verlag, New York.
<p>
<P>
<DD><DL>
<DT><B>Parameters:</B><DD><CODE>r</CODE> - must be > 0.<DD><CODE>k</CODE> - must be > 0.<DD><CODE>nr</CODE> - the number of the burr distribution (e.g. 3,4,5,6,9,12).</DL>
</DD>
</DL>
<HR>
<A NAME="nextCauchy(cern.jet.random.engine.RandomEngine)"><!-- --></A><H3>
nextCauchy</H3>
<PRE>
public static double <B>nextCauchy</B>(<A HREF="../../../cern/jet/random/engine/RandomEngine.html" title="class in cern.jet.random.engine">RandomEngine</A> randomGenerator)</PRE>
<DL>
<DD>Returns a cauchy distributed random number from the standard Cauchy distribution C(0,1).
<A HREF="http://www.cern.ch/RD11/rkb/AN16pp/node25.html#SECTION000250000000000000000"> math definition</A>
and <A HREF="http://www.statsoft.com/textbook/glosc.html#Cauchy Distribution"> animated definition</A>.
<p>
<tt>p(x) = 1/ (mean*pi * (1+(x/mean)^2))</tt>.
<p>
<b>Implementation:</b>
This is a port of <tt>cin.c</tt> from the <A HREF="http://www.cis.tu-graz.ac.at/stat/stadl/random.html">C-RAND / WIN-RAND</A> library.
<p>
<P>
<DD><DL>
</DL>
</DD>
</DL>
<HR>
<A NAME="nextErlang(double, double, cern.jet.random.engine.RandomEngine)"><!-- --></A><H3>
nextErlang</H3>
<PRE>
public static double <B>nextErlang</B>(double variance,
double mean,
<A HREF="../../../cern/jet/random/engine/RandomEngine.html" title="class in cern.jet.random.engine">RandomEngine</A> randomGenerator)</PRE>
<DL>
<DD>Returns an erlang distributed random number with the given variance and mean.
<P>
<DD><DL>
</DL>
</DD>
</DL>
<HR>
<A NAME="nextGeometric(double, cern.jet.random.engine.RandomEngine)"><!-- --></A><H3>
nextGeometric</H3>
<PRE>
public static int <B>nextGeometric</B>(double p,
<A HREF="../../../cern/jet/random/engine/RandomEngine.html" title="class in cern.jet.random.engine">RandomEngine</A> randomGenerator)</PRE>
<DL>
<DD>Returns a discrete geometric distributed random number; <A HREF="http://www.statsoft.com/textbook/glosf.html#Geometric Distribution">Definition</A>.
<p>
<tt>p(k) = p * (1-p)^k</tt> for <tt> k >= 0</tt>.
<p>
<b>Implementation:</b> Inversion method.
This is a port of <tt>geo.c</tt> from the <A HREF="http://www.cis.tu-graz.ac.at/stat/stadl/random.html">C-RAND / WIN-RAND</A> library.
<P>
<DD><DL>
<DT><B>Parameters:</B><DD><CODE>p</CODE> - must satisfy <tt>0 < p < 1</tt>.
<p></DL>
</DD>
</DL>
<HR>
<A NAME="nextLambda(double, double, cern.jet.random.engine.RandomEngine)"><!-- --></A><H3>
nextLambda</H3>
<PRE>
public static double <B>nextLambda</B>(double l3,
double l4,
<A HREF="../../../cern/jet/random/engine/RandomEngine.html" title="class in cern.jet.random.engine">RandomEngine</A> randomGenerator)</PRE>
<DL>
<DD>Returns a lambda distributed random number with parameters l3 and l4.
<p>
<b>Implementation:</b> Inversion method.
This is a port of <tt>lamin.c</tt> from the <A HREF="http://www.cis.tu-graz.ac.at/stat/stadl/random.html">C-RAND / WIN-RAND</A> library.
C-RAND's implementation, in turn, is based upon
<p>
J.S. Ramberg, B:W. Schmeiser (1974): An approximate method for generating asymmetric variables, Communications ACM 17, 78-82.
<p>
<P>
<DD><DL>
</DL>
</DD>
</DL>
<HR>
<A NAME="nextLaplace(cern.jet.random.engine.RandomEngine)"><!-- --></A><H3>
nextLaplace</H3>
<PRE>
public static double <B>nextLaplace</B>(<A HREF="../../../cern/jet/random/engine/RandomEngine.html" title="class in cern.jet.random.engine">RandomEngine</A> randomGenerator)</PRE>
<DL>
<DD>Returns a Laplace (Double Exponential) distributed random number from the standard Laplace distribution L(0,1).
<p>
<b>Implementation:</b> Inversion method.
This is a port of <tt>lapin.c</tt> from the <A HREF="http://www.cis.tu-graz.ac.at/stat/stadl/random.html">C-RAND / WIN-RAND</A> library.
<p>
<P>
<DD><DL>
</DL>
</DD>
</DL>
<HR>
<A NAME="nextLogistic(cern.jet.random.engine.RandomEngine)"><!-- --></A><H3>
nextLogistic</H3>
<PRE>
public static double <B>nextLogistic</B>(<A HREF="../../../cern/jet/random/engine/RandomEngine.html" title="class in cern.jet.random.engine">RandomEngine</A> randomGenerator)</PRE>
<DL>
<DD>Returns a random number from the standard Logistic distribution Log(0,1).
<p>
<b>Implementation:</b> Inversion method.
This is a port of <tt>login.c</tt> from the <A HREF="http://www.cis.tu-graz.ac.at/stat/stadl/random.html">C-RAND / WIN-RAND</A> library.
<P>
<DD><DL>
</DL>
</DD>
</DL>
<HR>
<A NAME="nextPowLaw(double, double, cern.jet.random.engine.RandomEngine)"><!-- --></A><H3>
nextPowLaw</H3>
<PRE>
public static double <B>nextPowLaw</B>(double alpha,
double cut,
<A HREF="../../../cern/jet/random/engine/RandomEngine.html" title="class in cern.jet.random.engine">RandomEngine</A> randomGenerator)</PRE>
<DL>
<DD>Returns a power-law distributed random number with the given exponent and lower cutoff.
<P>
<DD><DL>
<DT><B>Parameters:</B><DD><CODE>alpha</CODE> - the exponent<DD><CODE>cut</CODE> - the lower cutoff</DL>
</DD>
</DL>
<HR>
<A NAME="nextTriangular(cern.jet.random.engine.RandomEngine)"><!-- --></A><H3>
nextTriangular</H3>
<PRE>
public static double <B>nextTriangular</B>(<A HREF="../../../cern/jet/random/engine/RandomEngine.html" title="class in cern.jet.random.engine">RandomEngine</A> randomGenerator)</PRE>
<DL>
<DD>Returns a random number from the standard Triangular distribution in (-1,1).
<p>
<b>Implementation:</b> Inversion method.
This is a port of <tt>tra.c</tt> from the <A HREF="http://www.cis.tu-graz.ac.at/stat/stadl/random.html">C-RAND / WIN-RAND</A> library.
<p>
<P>
<DD><DL>
</DL>
</DD>
</DL>
<HR>
<A NAME="nextWeibull(double, double, cern.jet.random.engine.RandomEngine)"><!-- --></A><H3>
nextWeibull</H3>
<PRE>
public static double <B>nextWeibull</B>(double alpha,
double beta,
<A HREF="../../../cern/jet/random/engine/RandomEngine.html" title="class in cern.jet.random.engine">RandomEngine</A> randomGenerator)</PRE>
<DL>
<DD>Returns a weibull distributed random number.
Polar method.
See Simulation, Modelling & Analysis by Law & Kelton, pp259
<P>
<DD><DL>
</DL>
</DD>
</DL>
<HR>
<A NAME="nextZipfInt(double, cern.jet.random.engine.RandomEngine)"><!-- --></A><H3>
nextZipfInt</H3>
<PRE>
public static int <B>nextZipfInt</B>(double z,
<A HREF="../../../cern/jet/random/engine/RandomEngine.html" title="class in cern.jet.random.engine">RandomEngine</A> randomGenerator)</PRE>
<DL>
<DD>Returns a zipfian distributed random number with the given skew.
<p>
Algorithm from page 551 of:
Devroye, Luc (1986) `Non-uniform random variate generation',
Springer-Verlag: Berlin. ISBN 3-540-96305-7 (also 0-387-96305-7)
<P>
<DD><DL>
<DT><B>Parameters:</B><DD><CODE>z</CODE> - the skew of the distribution (must be >1.0).</DL>
</DD>
</DL>
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