Package jline.lang.processes

Class ME

  • All Implemented Interfaces:
    java.io.Serializable , jline.lang.Copyable 
    
public class ME
extends Markovian

    A Matrix Exponential (ME) distribution. ME distributions are characterized by an initial vector alpha and a matrix parameter A. They generalize Phase-Type (PH) distributions by allowing alpha to have entries outside [0,1] and A to have arbitrary structure (not necessarily a valid sub-generator). Representation: - alpha: initial vector (may have negative entries or sum != 1) - A: matrix parameter (must have all eigenvalues with negative real parts) - Dominant eigenvalue of A must be negative and real The distribution function is: F(t) = 1 - alpha * exp(A*t) * e (under certain conditions) Moments: m_k = k! * alpha * (-A)^(-k) * e

    • Nested Class Summary

      Nested Classes 
      Modifier and Type Class Description

    • Constructor Summary

      Constructors 
      Constructor Description
      ME(Matrix alpha, Matrix A) Creates a Matrix Exponential distribution with specified initial vector and matrix parameter.

    • Enum Constant Summary

      Enum Constants 
      Enum Constant Description

    • Method Summary

      Modifier and Type Method Description
      Matrix getAlpha() Gets the initial vector alpha.
      Matrix getA() Gets the matrix parameter A.
      long getNumberOfPhases() Gets the number of phases in this Markovian distribution.
      MatrixCell getProcess() Gets the matrix representation of this Markovian process.
      static ME fitMoments(Array<double> moments) Creates an ME distribution by fitting the given moments.
      static ME fromExp(double rate) Creates an ME distribution from an exponential distribution.
      static ME fromErlang(int k, double rate) Creates an ME distribution from an Erlang distribution.
      static ME fromHyperExp(Array<double> p, Array<double> rates) Creates an ME distribution from a HyperExponential distribution.

      • Methods inherited from class jline.lang.processes.Markovian

        D, acf, embedded, embeddedProb, evalCDF, evalCDF, evalLST, evalMeanT, evalVarT, getACF, getEmbedded, getEmbeddedProb, getIDC, getIDI, getInitProb, getMean, getMoments, getMu, getPhi, getRate, getSCV, getSkewness, getSubgenerator, getVar, getVariance, idc, idi, initProb, mean, moments, mu, numPhases, numberOfPhases, phi, process, rate, sample, sample, scv, setMean, setProcess, setRate, skewness, subgenerator, var, variance

      • Methods inherited from class jline.lang.processes.Distribution

        evalProbInterval, getName, getNumParams, getParam, getSupport, isContinuous, isDisabled, isDiscrete, isImmediate, isMarkovian, name, numParams, param, setNumParams, setParam, support

      • Methods inherited from class jline.lang.Copyable

        copy

      • Methods inherited from class java.lang.Object

        clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

    • Constructor Detail

      • ME

        ME(Matrix alpha, Matrix A)
        Creates a Matrix Exponential distribution with specified initial vector and matrix parameter.
        Parameters:
        alpha - the initial vector (row vector as Matrix)
        A - the matrix parameter (must be square with negative real eigenvalues)

    • Method Detail

      • getAlpha

         Matrix getAlpha()

        Gets the initial vector alpha.

        Returns:

        the initial vector as a Matrix

      • getA

         Matrix getA()

        Gets the matrix parameter A.

        Returns:

        the matrix parameter A

      • getNumberOfPhases

         long getNumberOfPhases()

        Gets the number of phases in this Markovian distribution.

        Returns:

        the number of phases

      • getProcess

         MatrixCell getProcess()

        Gets the matrix representation of this Markovian process.

        Returns:

        MatrixCell containing D0, D1, ... matrices

      • fitMoments

         static ME fitMoments(Array<double> moments)

        Creates an ME distribution by fitting the given moments. Uses BuTools MEFromMoments algorithm.

        Parameters:
        moments - array of moments (requires 2*M-1 moments for order M ME distribution)
        Returns:

        an ME distribution matching the given moments

      • fromExp

         static ME fromExp(double rate)

        Creates an ME distribution from an exponential distribution. This is a convenience method showing that Exp is a special case of ME.

        Parameters:
        rate - the rate parameter (lambda)
        Returns:

        an ME distribution equivalent to Exp(rate)

      • fromErlang

         static ME fromErlang(int k, double rate)

        Creates an ME distribution from an Erlang distribution. This is a convenience method showing that Erlang is a special case of ME.

        Parameters:
        k - number of phases
        rate - rate parameter for each phase
        Returns:

        an ME distribution equivalent to Erlang(k, rate)

      • fromHyperExp

         static ME fromHyperExp(Array<double> p, Array<double> rates)

        Creates an ME distribution from a HyperExponential distribution. This is a convenience method showing that HyperExp is a special case of ME.

        Parameters:
        p - array of probabilities for each branch
        rates - array of rates for each branch
        Returns:

        an ME distribution equivalent to HyperExp(p, rates)