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<H2>
Package cern.jet.random
</H2>
Large variety of probability distributions featuring high performance generation 
 of random numbers, CDF's and PDF's.

See:
 
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<A HREF="#package_description">Description</A>

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<TD COLSPAN=2>
Class Summary</TD>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD WIDTH="15%"><A HREF="../../../cern/jet/random/AbstractContinousDistribution.html" title="class in cern.jet.random">AbstractContinousDistribution</A></TD>
<TD>Abstract base class for all continous distributions.</TD>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD WIDTH="15%"><A HREF="../../../cern/jet/random/AbstractDiscreteDistribution.html" title="class in cern.jet.random">AbstractDiscreteDistribution</A></TD>
<TD>Abstract base class for all discrete distributions.</TD>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD WIDTH="15%"><A HREF="../../../cern/jet/random/AbstractDistribution.html" title="class in cern.jet.random">AbstractDistribution</A></TD>
<TD>Abstract base class for all random distributions.</TD>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD WIDTH="15%"><A HREF="../../../cern/jet/random/Benchmark.html" title="class in cern.jet.random">Benchmark</A></TD>
<TD>Benchmarks random number generation from various distributions as well as PDF and CDF lookups.</TD>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD WIDTH="15%"><A HREF="../../../cern/jet/random/Beta.html" title="class in cern.jet.random">Beta</A></TD>
<TD>Beta distribution; <A HREF="http://www.cern.ch/RD11/rkb/AN16pp/node15.html#SECTION000150000000000000000"> math definition</A>
 and <A HREF="http://www.statsoft.com/textbook/glosb.html#Beta Distribution"> animated definition</A>.</TD>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD WIDTH="15%"><A HREF="../../../cern/jet/random/Binomial.html" title="class in cern.jet.random">Binomial</A></TD>
<TD>Binomial distribution; See the <A HREF="http://www.cern.ch/RD11/rkb/AN16pp/node19.html#SECTION000190000000000000000"> math definition</A>
 and <A HREF="http://www.statsoft.com/textbook/glosb.html#Binomial Distribution"> animated definition</A>.</TD>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD WIDTH="15%"><A HREF="../../../cern/jet/random/BreitWigner.html" title="class in cern.jet.random">BreitWigner</A></TD>
<TD>BreitWigner (aka Lorentz) distribution; See the <A HREF="http://www.cern.ch/RD11/rkb/AN16pp/node23.html#SECTION000230000000000000000"> math definition</A>.</TD>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD WIDTH="15%"><A HREF="../../../cern/jet/random/BreitWignerMeanSquare.html" title="class in cern.jet.random">BreitWignerMeanSquare</A></TD>
<TD>Mean-square BreitWigner distribution; See the <A HREF="http://www.cern.ch/RD11/rkb/AN16pp/node23.html#SECTION000230000000000000000"> math definition</A>.</TD>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD WIDTH="15%"><A HREF="../../../cern/jet/random/ChiSquare.html" title="class in cern.jet.random">ChiSquare</A></TD>
<TD>ChiSquare distribution; See the <A HREF="http://www.cern.ch/RD11/rkb/AN16pp/node31.html#SECTION000310000000000000000"> math definition</A>
 and <A HREF="http://www.statsoft.com/textbook/glosc.html#Chi-square Distribution"> animated definition</A>.</TD>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD WIDTH="15%"><A HREF="../../../cern/jet/random/Distributions.html" title="class in cern.jet.random">Distributions</A></TD>
<TD>Contains methods for conveniently generating pseudo-random numbers from special distributions such as the Burr, Cauchy, Erlang, Geometric, Lambda, Laplace, Logistic, Weibull, etc.</TD>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD WIDTH="15%"><A HREF="../../../cern/jet/random/Empirical.html" title="class in cern.jet.random">Empirical</A></TD>
<TD>Empirical distribution.</TD>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD WIDTH="15%"><A HREF="../../../cern/jet/random/EmpiricalWalker.html" title="class in cern.jet.random">EmpiricalWalker</A></TD>
<TD>Discrete Empirical distribution (pdf's can be specified).</TD>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD WIDTH="15%"><A HREF="../../../cern/jet/random/Exponential.html" title="class in cern.jet.random">Exponential</A></TD>
<TD>Exponential Distribution (aka Negative Exponential Distribution); See the <A HREF="http://www.cern.ch/RD11/rkb/AN16pp/node78.html#SECTION000780000000000000000"> math definition</A>
 <A HREF="http://www.statsoft.com/textbook/glose.html#Exponential Distribution"> animated definition</A>.</TD>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD WIDTH="15%"><A HREF="../../../cern/jet/random/ExponentialPower.html" title="class in cern.jet.random">ExponentialPower</A></TD>
<TD>Exponential Power distribution.</TD>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD WIDTH="15%"><A HREF="../../../cern/jet/random/Gamma.html" title="class in cern.jet.random">Gamma</A></TD>
<TD>Gamma distribution; <A HREF="http://wwwinfo.cern.ch/asdoc/shortwrupsdir/g106/top.html"> math definition</A>,
 <A HREF="http://www.cern.ch/RD11/rkb/AN16pp/node96.html#SECTION000960000000000000000"> definition of gamma function</A>
 and <A HREF="http://www.statsoft.com/textbook/glosf.html#Gamma Distribution"> animated definition</A>.</TD>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD WIDTH="15%"><A HREF="../../../cern/jet/random/Hyperbolic.html" title="class in cern.jet.random">Hyperbolic</A></TD>
<TD>Hyperbolic distribution.</TD>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD WIDTH="15%"><A HREF="../../../cern/jet/random/HyperGeometric.html" title="class in cern.jet.random">HyperGeometric</A></TD>
<TD>HyperGeometric distribution; See the <A HREF="http://library.advanced.org/10030/6atpdvah.htm"> math definition</A>
 
 The hypergeometric distribution with parameters <tt>N</tt>, <tt>n</tt> and <tt>s</tt> is the probability distribution of the random variable X, 
 whose value is the number of successes in a sample of <tt>n</tt> items from a population of size <tt>N</tt> that has <tt>s</tt> 'success' items and <tt>N - s</tt> 'failure' items.</TD>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD WIDTH="15%"><A HREF="../../../cern/jet/random/Logarithmic.html" title="class in cern.jet.random">Logarithmic</A></TD>
<TD>Logarithmic distribution.</TD>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD WIDTH="15%"><A HREF="../../../cern/jet/random/NegativeBinomial.html" title="class in cern.jet.random">NegativeBinomial</A></TD>
<TD>Negative Binomial distribution; See the <A HREF="http://www.statlets.com/usermanual/glossary2.htm"> math definition</A>.</TD>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD WIDTH="15%"><A HREF="../../../cern/jet/random/Normal.html" title="class in cern.jet.random">Normal</A></TD>
<TD>Normal (aka Gaussian) distribution; See the <A HREF="http://www.cern.ch/RD11/rkb/AN16pp/node188.html#SECTION0001880000000000000000"> math definition</A>
and <A HREF="http://www.statsoft.com/textbook/glosn.html#Normal Distribution"> animated definition</A>.</TD>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD WIDTH="15%"><A HREF="../../../cern/jet/random/Poisson.html" title="class in cern.jet.random">Poisson</A></TD>
<TD>Poisson distribution (quick); See the <A HREF="http://www.cern.ch/RD11/rkb/AN16pp/node208.html#SECTION0002080000000000000000"> math definition</A>
 and <A HREF="http://www.statsoft.com/textbook/glosp.html#Poisson Distribution"> animated definition</A>.</TD>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD WIDTH="15%"><A HREF="../../../cern/jet/random/PoissonSlow.html" title="class in cern.jet.random">PoissonSlow</A></TD>
<TD>Poisson distribution; See the <A HREF="http://www.cern.ch/RD11/rkb/AN16pp/node208.html#SECTION0002080000000000000000"> math definition</A>
 and <A HREF="http://www.statsoft.com/textbook/glosp.html#Poisson Distribution"> animated definition</A>.</TD>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD WIDTH="15%"><A HREF="../../../cern/jet/random/StudentT.html" title="class in cern.jet.random">StudentT</A></TD>
<TD>StudentT distribution (aka T-distribution); See the <A HREF="http://www.cern.ch/RD11/rkb/AN16pp/node279.html#SECTION0002790000000000000000"> math definition</A>
 and <A HREF="http://www.statsoft.com/textbook/gloss.html#Student's t Distribution"> animated definition</A>.</TD>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD WIDTH="15%"><A HREF="../../../cern/jet/random/Uniform.html" title="class in cern.jet.random">Uniform</A></TD>
<TD>Uniform distribution; <A HREF="http://www.cern.ch/RD11/rkb/AN16pp/node292.html#SECTION0002920000000000000000"> Math definition</A>
 and <A HREF="http://www.statsoft.com/textbook/glosu.html#Uniform Distribution"> animated definition</A>.</TD>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD WIDTH="15%"><A HREF="../../../cern/jet/random/VonMises.html" title="class in cern.jet.random">VonMises</A></TD>
<TD>Von Mises distribution.</TD>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD WIDTH="15%"><A HREF="../../../cern/jet/random/Zeta.html" title="class in cern.jet.random">Zeta</A></TD>
<TD>Zeta distribution.</TD>
</TR>
</TABLE>
&nbsp;

<A NAME="package_description"></A><H2>
Package cern.jet.random Description
</H2>

Large variety of probability distributions featuring high performance generation 
 of random numbers, CDF's and PDF's.
You can always do a quick and dirty check to test the properties of any given distribution, for example, as follows:
<table>
<td class="PRE"> 
<pre>
// Gamma distribution

// define distribution parameters
double mean = 5;
double variance = 1.5;
double alpha = mean*mean / variance; 
double lambda = 1 / (variance / mean);

// for tests and debugging use a random engine with CONSTANT seed --> deterministic and reproducible results
cern.jet.random.engine.RandomEngine engine = new cern.jet.random.engine.MersenneTwister();

// your favourite distribution goes here
cern.jet.random.AbstractDistribution dist = new cern.jet.random.Gamma(alpha,lambda,engine);

// collect random numbers and print statistics
int size = 100000;
cern.colt.list.DoubleArrayList numbers = new cern.colt.list.DoubleArrayList(size);
for (int i=0; i < size; i++) numbers.add(dist.nextDouble());

hep.aida.bin.DynamicBin1D bin = new hep.aida.bin.DynamicBin1D();
bin.addAllOf(numbers);
System.out.println(bin);

Will print something like

Size: 100000
Sum: 499830.30147620925
SumOfSquares: 2648064.0189520954
Min: 1.2903021480010035
Max: 12.632626684290546
Mean: 4.998303014762093
RMS: 5.14593433591228
Variance: 1.497622138362513
Standard deviation: 1.2237737284165373
Standard error: 0.0038699123224725817
Geometric mean: 4.849381516061957
Product: Infinity
Harmonic mean: 4.69916104903662
Sum of inversions: 21280.394299425236
Skew: 0.49097523334186227
Kurtosis: 0.3461005384481113
Sum of powers(3): 1.4822908764628284E7
Sum of powers(4): 8.741360251658581E7
Sum of powers(5): 5.41658186456702E8
Sum of powers(6): 3.5183920126086535E9
Moment(0,0): 1.0
Moment(1,0): 4.998303014762093
Moment(2,0): 26.480640189520955
Moment(3,0): 148.22908764628284
Moment(4,0): 874.1360251658581
Moment(5,0): 5416.58186456702
Moment(6,0): 35183.92012608654
Moment(0,mean()): 1.0
Moment(1,mean()): 3.7017002796346785E-14
Moment(2,mean()): 1.4976071621409774
Moment(3,mean()): 0.8998351672510565
Moment(4,mean()): 7.50487543880015
Moment(5,mean()): 14.413483695698101
Moment(6,mean()): 77.72119325586715
25%, 50%, 75% Quantiles: 4.122365795016783, 4.897730017566362, 5.763097174551738
quantileInverse(median): 0.500005
Distinct elements & frequencies not printed (too many).
</pre>
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Rabbit simulation

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