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<H2>

cern.jet.random
 
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">cern.jet.random.Distributions
</PRE>
<HR>
<DL>
<DT>public class Distributions<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>

Contains methods for conveniently generating pseudo-random numbers from special distributions such as the Burr, Cauchy, Erlang, Geometric, Lambda, Laplace, Logistic, Weibull, etc.
 
 About this class:
 <dt>All distributions are obtained by using a uniform pseudo-random number generator.
 followed by a transformation to the desired distribution.
 
 Example usage:<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>

<DL>
<DT>Version:</DT>
 <DD>1.0, 09/24/99</DD>
<DT>See Also:<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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Method Summary</TD>
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<CODE>static&nbsp;double</CODE></TD>
<TD><CODE><A HREF="../../../cern/jet/random/Distributions.html#geometricPdf(int, double)">geometricPdf</A>(int&nbsp;k,
 double&nbsp;p)</CODE>

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Returns the probability distribution function of the discrete geometric distribution.</TD>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD ALIGN="right" VALIGN="top" WIDTH="1%">
<CODE>static&nbsp;double</CODE></TD>
<TD><CODE><A HREF="../../../cern/jet/random/Distributions.html#nextBurr1(double, int, cern.jet.random.engine.RandomEngine)">nextBurr1</A>(double&nbsp;r,
 int&nbsp;nr,
 <A HREF="../../../cern/jet/random/engine/RandomEngine.html" title="class in cern.jet.random.engine">RandomEngine</A>&nbsp;randomGenerator)</CODE>

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;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%">
<CODE>static&nbsp;double</CODE></TD>
<TD><CODE><A HREF="../../../cern/jet/random/Distributions.html#nextBurr2(double, double, int, cern.jet.random.engine.RandomEngine)">nextBurr2</A>(double&nbsp;r,
 double&nbsp;k,
 int&nbsp;nr,
 <A HREF="../../../cern/jet/random/engine/RandomEngine.html" title="class in cern.jet.random.engine">RandomEngine</A>&nbsp;randomGenerator)</CODE>

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;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%">
<CODE>static&nbsp;double</CODE></TD>
<TD><CODE><A HREF="../../../cern/jet/random/Distributions.html#nextCauchy(cern.jet.random.engine.RandomEngine)">nextCauchy</A>(<A HREF="../../../cern/jet/random/engine/RandomEngine.html" title="class in cern.jet.random.engine">RandomEngine</A>&nbsp;randomGenerator)</CODE>

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;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%">
<CODE>static&nbsp;double</CODE></TD>
<TD><CODE><A HREF="../../../cern/jet/random/Distributions.html#nextErlang(double, double, cern.jet.random.engine.RandomEngine)">nextErlang</A>(double&nbsp;variance,
 double&nbsp;mean,
 <A HREF="../../../cern/jet/random/engine/RandomEngine.html" title="class in cern.jet.random.engine">RandomEngine</A>&nbsp;randomGenerator)</CODE>

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Returns an erlang distributed random number with the given variance and mean.</TD>
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<TR BGCOLOR="white" CLASS="TableRowColor">
<TD ALIGN="right" VALIGN="top" WIDTH="1%">
<CODE>static&nbsp;int</CODE></TD>
<TD><CODE><A HREF="../../../cern/jet/random/Distributions.html#nextGeometric(double, cern.jet.random.engine.RandomEngine)">nextGeometric</A>(double&nbsp;p,
 <A HREF="../../../cern/jet/random/engine/RandomEngine.html" title="class in cern.jet.random.engine">RandomEngine</A>&nbsp;randomGenerator)</CODE>

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;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%">
<CODE>static&nbsp;double</CODE></TD>
<TD><CODE><A HREF="../../../cern/jet/random/Distributions.html#nextLambda(double, double, cern.jet.random.engine.RandomEngine)">nextLambda</A>(double&nbsp;l3,
 double&nbsp;l4,
 <A HREF="../../../cern/jet/random/engine/RandomEngine.html" title="class in cern.jet.random.engine">RandomEngine</A>&nbsp;randomGenerator)</CODE>

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Returns a lambda distributed random number with parameters l3 and l4.</TD>
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<TR BGCOLOR="white" CLASS="TableRowColor">
<TD ALIGN="right" VALIGN="top" WIDTH="1%">
<CODE>static&nbsp;double</CODE></TD>
<TD><CODE><A HREF="../../../cern/jet/random/Distributions.html#nextLaplace(cern.jet.random.engine.RandomEngine)">nextLaplace</A>(<A HREF="../../../cern/jet/random/engine/RandomEngine.html" title="class in cern.jet.random.engine">RandomEngine</A>&nbsp;randomGenerator)</CODE>

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;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%">
<CODE>static&nbsp;double</CODE></TD>
<TD><CODE><A HREF="../../../cern/jet/random/Distributions.html#nextLogistic(cern.jet.random.engine.RandomEngine)">nextLogistic</A>(<A HREF="../../../cern/jet/random/engine/RandomEngine.html" title="class in cern.jet.random.engine">RandomEngine</A>&nbsp;randomGenerator)</CODE>

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;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%">
<CODE>static&nbsp;double</CODE></TD>
<TD><CODE><A HREF="../../../cern/jet/random/Distributions.html#nextPowLaw(double, double, cern.jet.random.engine.RandomEngine)">nextPowLaw</A>(double&nbsp;alpha,
 double&nbsp;cut,
 <A HREF="../../../cern/jet/random/engine/RandomEngine.html" title="class in cern.jet.random.engine">RandomEngine</A>&nbsp;randomGenerator)</CODE>

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;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%">
<CODE>static&nbsp;double</CODE></TD>
<TD><CODE><A HREF="../../../cern/jet/random/Distributions.html#nextTriangular(cern.jet.random.engine.RandomEngine)">nextTriangular</A>(<A HREF="../../../cern/jet/random/engine/RandomEngine.html" title="class in cern.jet.random.engine">RandomEngine</A>&nbsp;randomGenerator)</CODE>

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;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%">
<CODE>static&nbsp;double</CODE></TD>
<TD><CODE><A HREF="../../../cern/jet/random/Distributions.html#nextWeibull(double, double, cern.jet.random.engine.RandomEngine)">nextWeibull</A>(double&nbsp;alpha,
 double&nbsp;beta,
 <A HREF="../../../cern/jet/random/engine/RandomEngine.html" title="class in cern.jet.random.engine">RandomEngine</A>&nbsp;randomGenerator)</CODE>

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Returns a weibull distributed random number.</TD>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD ALIGN="right" VALIGN="top" WIDTH="1%">
<CODE>static&nbsp;int</CODE></TD>
<TD><CODE><A HREF="../../../cern/jet/random/Distributions.html#nextZipfInt(double, cern.jet.random.engine.RandomEngine)">nextZipfInt</A>(double&nbsp;z,
 <A HREF="../../../cern/jet/random/engine/RandomEngine.html" title="class in cern.jet.random.engine">RandomEngine</A>&nbsp;randomGenerator)</CODE>

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Returns a zipfian distributed random number with the given skew.</TD>
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Method Detail</TD>
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<A NAME="geometricPdf(int, double)"></A><H3>
geometricPdf</H3>
<PRE>
public static double geometricPdf(int&nbsp;k,
 double&nbsp;p)</PRE>
<DL>
<DD>Returns the probability distribution function of the discrete geometric distribution.
 
 <tt>p(k) = p * (1-p)^k</tt> for <tt> k &gt;= 0</tt>.
 

<DD><DL>
<DT>Parameters:<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 nextBurr1(double&nbsp;r,
 int&nbsp;nr,
 <A HREF="../../../cern/jet/random/engine/RandomEngine.html" title="class in cern.jet.random.engine">RandomEngine</A>&nbsp;randomGenerator)</PRE>
<DL>
<DD>Returns a random number from the Burr II, VII, VIII, X Distributions.
 
 Implementation: 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
 
 L. Devroye (1986): Non-Uniform Random Variate Generation, Springer Verlag, New York. 
 

<DD><DL>
<DT>Parameters:<DD><CODE>r</CODE> - must be &gt; 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 nextBurr2(double&nbsp;r,
 double&nbsp;k,
 int&nbsp;nr,
 <A HREF="../../../cern/jet/random/engine/RandomEngine.html" title="class in cern.jet.random.engine">RandomEngine</A>&nbsp;randomGenerator)</PRE>
<DL>
<DD>Returns a random number from the Burr III, IV, V, VI, IX, XII distributions.
 
 Implementation: 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
 
 L. Devroye (1986): Non-Uniform Random Variate Generation, Springer Verlag, New York. 
 

<DD><DL>
<DT>Parameters:<DD><CODE>r</CODE> - must be &gt; 0.<DD><CODE>k</CODE> - must be &gt; 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 nextCauchy(<A HREF="../../../cern/jet/random/engine/RandomEngine.html" title="class in cern.jet.random.engine">RandomEngine</A>&nbsp;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>. 
 
 <tt>p(x) = 1/ (mean*pi * (1+(x/mean)^2))</tt>.
 
 Implementation:
 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.
 

<DD><DL>
</DL>
</DD>
</DL>
<HR>

<A NAME="nextErlang(double, double, cern.jet.random.engine.RandomEngine)"></A><H3>
nextErlang</H3>
<PRE>
public static double nextErlang(double&nbsp;variance,
 double&nbsp;mean,
 <A HREF="../../../cern/jet/random/engine/RandomEngine.html" title="class in cern.jet.random.engine">RandomEngine</A>&nbsp;randomGenerator)</PRE>
<DL>
<DD>Returns an erlang distributed random number with the given variance and mean.

<DD><DL>
</DL>
</DD>
</DL>
<HR>

<A NAME="nextGeometric(double, cern.jet.random.engine.RandomEngine)"></A><H3>
nextGeometric</H3>
<PRE>
public static int nextGeometric(double&nbsp;p,
 <A HREF="../../../cern/jet/random/engine/RandomEngine.html" title="class in cern.jet.random.engine">RandomEngine</A>&nbsp;randomGenerator)</PRE>
<DL>
<DD>Returns a discrete geometric distributed random number; <A HREF="http://www.statsoft.com/textbook/glosf.html#Geometric Distribution">Definition</A>.
 
 <tt>p(k) = p * (1-p)^k</tt> for <tt> k &gt;= 0</tt>.
 
 Implementation: 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.

<DD><DL>
<DT>Parameters:<DD><CODE>p</CODE> - must satisfy <tt>0 &lt; p &lt; 1</tt>.
 </DL>
</DD>
</DL>
<HR>

<A NAME="nextLambda(double, double, cern.jet.random.engine.RandomEngine)"></A><H3>
nextLambda</H3>
<PRE>
public static double nextLambda(double&nbsp;l3,
 double&nbsp;l4,
 <A HREF="../../../cern/jet/random/engine/RandomEngine.html" title="class in cern.jet.random.engine">RandomEngine</A>&nbsp;randomGenerator)</PRE>
<DL>
<DD>Returns a lambda distributed random number with parameters l3 and l4.
 
 Implementation: 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
 
 J.S. Ramberg, B:W. Schmeiser (1974): An approximate method for generating asymmetric variables, Communications ACM 17, 78-82.
 

<DD><DL>
</DL>
</DD>
</DL>
<HR>

<A NAME="nextLaplace(cern.jet.random.engine.RandomEngine)"></A><H3>
nextLaplace</H3>
<PRE>
public static double nextLaplace(<A HREF="../../../cern/jet/random/engine/RandomEngine.html" title="class in cern.jet.random.engine">RandomEngine</A>&nbsp;randomGenerator)</PRE>
<DL>
<DD>Returns a Laplace (Double Exponential) distributed random number from the standard Laplace distribution L(0,1). 
 
 Implementation: 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.
 

<DD><DL>
</DL>
</DD>
</DL>
<HR>

<A NAME="nextLogistic(cern.jet.random.engine.RandomEngine)"></A><H3>
nextLogistic</H3>
<PRE>
public static double nextLogistic(<A HREF="../../../cern/jet/random/engine/RandomEngine.html" title="class in cern.jet.random.engine">RandomEngine</A>&nbsp;randomGenerator)</PRE>
<DL>
<DD>Returns a random number from the standard Logistic distribution Log(0,1).
 
 Implementation: 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.

<DD><DL>
</DL>
</DD>
</DL>
<HR>

<A NAME="nextPowLaw(double, double, cern.jet.random.engine.RandomEngine)"></A><H3>
nextPowLaw</H3>
<PRE>
public static double nextPowLaw(double&nbsp;alpha,
 double&nbsp;cut,
 <A HREF="../../../cern/jet/random/engine/RandomEngine.html" title="class in cern.jet.random.engine">RandomEngine</A>&nbsp;randomGenerator)</PRE>
<DL>
<DD>Returns a power-law distributed random number with the given exponent and lower cutoff.

<DD><DL>
<DT>Parameters:<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 nextTriangular(<A HREF="../../../cern/jet/random/engine/RandomEngine.html" title="class in cern.jet.random.engine">RandomEngine</A>&nbsp;randomGenerator)</PRE>
<DL>
<DD>Returns a random number from the standard Triangular distribution in (-1,1).
 
 Implementation: 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.
 

<DD><DL>
</DL>
</DD>
</DL>
<HR>

<A NAME="nextWeibull(double, double, cern.jet.random.engine.RandomEngine)"></A><H3>
nextWeibull</H3>
<PRE>
public static double nextWeibull(double&nbsp;alpha,
 double&nbsp;beta,
 <A HREF="../../../cern/jet/random/engine/RandomEngine.html" title="class in cern.jet.random.engine">RandomEngine</A>&nbsp;randomGenerator)</PRE>
<DL>
<DD>Returns a weibull distributed random number. 
 Polar method.
 See Simulation, Modelling & Analysis by Law & Kelton, pp259

<DD><DL>
</DL>
</DD>
</DL>
<HR>

<A NAME="nextZipfInt(double, cern.jet.random.engine.RandomEngine)"></A><H3>
nextZipfInt</H3>
<PRE>
public static int nextZipfInt(double&nbsp;z,
 <A HREF="../../../cern/jet/random/engine/RandomEngine.html" title="class in cern.jet.random.engine">RandomEngine</A>&nbsp;randomGenerator)</PRE>
<DL>
<DD>Returns a zipfian distributed random number with the given skew.
 
 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)

<DD><DL>
<DT>Parameters:<DD><CODE>z</CODE> - the skew of the distribution (must be &gt;1.0).</DL>
</DD>
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Rabbit simulation

initial commit