## Package Statistics

Package description: `Statistics`

See:
Description

 Class Summary BasicHistogram Basic histogram of a random variable able to write ASCII character output which can then be processed by Scigraphica or gri (a graphics programming language) into a postscript histogram. ControlledRandomVariable Class improving the convergence of conditional expectations in the class `RandomVariable` by the use of control variates. EmpiricalDistribution Container for data implementing a large number of efficient statistics. EmpiricalRandomVariable A random variable X distributed according to the empirical distribution associated with a data sample. FinMath This class contains static methods to compute functions or solve eqations * useful in basic financial mathematics. FixedBinDataSource A non rebinnable container for data implementing the interface `jas.hist.Rebinnable1DHistogramData` defined in the JAS library. LoopStatus Provides methods to report the progress of a loop and project time to completion. PointDataSource Class used to draw a single vertical line in a `jas.hist.JASHist` histogram. PoissonVariable The Poisson variable N with intensity (mean) lambda has values n>=0 * with probabilities p_n=Prob(N=n)=e^{-lambda}*lambda^n/n!. Random Provides static methods to generate random numbers based on the * cern.jet.random random number generators. RandomDataSource A normalized `FixedBinDataSource` fed by the samples of a random variable X conditioned on information available at time t. RandomVariable This class implements methods to compute conditional and unconditional expectations, standard deviations and other statistics and histograms of a random variable X (`this`). RandomVector This class is the vectorial analogue of the class `RandomVariable` and implements componentwise expectations and standard deviations as well as covariations and correlations between components. RandVariable A restricted version of the class `RandomVariable` providing * only one method to compute the mean. Vector Provides static methods for component by component operations on double[ ]s.

## Package description: `Statistics`

This is the main package defining `RandomVariables` and `RandomVectors`. Each of these classes becomes concrete by defining a single abstract method `getValue(int t)` intepreted as the next draw from the underlying distribution conditioned on all information available at time `t`. Typically this information is the state of the path `sε[0,t]-> X(s)` of some stochastic process `X` up to time `t`.

Random variables and vectors have a variety of methods to compute statistics associated with the underlying distribution. Histograms are also supported. Random vectors are necessary if we have to deal with correlations and have a method to compute the covariation matrix. One call to the underlying stochastic mechanism produces the next sample for each coordinate. Separate random variables make separate calls to the underlying stochastic mechanism and thus appear to be independent.

There is also a utility class `FinMath` containing some static methods which are useful in financial mathematics: the Black-Scholes formula, solving for implied volatlities, cumulative normal and inverse cumulative normal distribution function etc.

The various `data source` classes make the connection to the `jas` (java analyis studio) library to support the computation and display of histograms.