Package jline.lang.processes

Class PH

java.lang.Object

jline.lang.processes.Distribution

jline.lang.processes.ContinuousDistribution

jline.lang.processes.Markovian

jline.lang.processes.PH

All Implemented Interfaces:

Serializable, Copyable

public class PH
extends Markovian

A general phase-type (PH) distribution

See Also:

• Serialized Form

Field Summary

Fields inherited from class jline.lang.processes.Markovian

nPhases, process

Fields inherited from class jline.lang.processes.Distribution

immediate, mean, name, numParam, params, support

Constructor Summary

Constructors

Constructor	Description
PH(Matrix alpha, Matrix T)

Method Summary

Modifier and Type	Method	Description
double	evalCDF(double t)	Evaluates the cumulative distribution function (CDF) at time t.
double	evalLST(double s)	Evaluate the Laplace-Stieltjes Transform at s
static PH	fit(double mean, double scv, double skew)	Fits a PH from the mean, the squared coefficient of variation and the skewness.
static PH	fitCentral(double mean, double var, double skew)	Fits a PH from the mean, the variance and the skewness.
static PH	fitMeanAndSCV(double mean, double scv)	Fits a PH from the mean and the squared coefficient of variation, taking the minimum-skewness third moment of the acyclic class.
static PH	fitRawMoments(double m1, double m2, double m3)	Fits a PH from the first three raw moments.
Matrix	getInitProb()	Gets the initial probability vector.
double	getMean()	Gets the mean of this Markovian distribution.
long	getNumberOfPhases()	Gets the number of phases in this Markovian distribution.
MatrixCell	getProcess()	Gets the matrix representation of this Markovian process.
double	getRate()	Gets the rate of this distribution (inverse of mean).
double	getSCV()	Gets the squared coefficient of variation (SCV) of this distribution.
double	getSkewness()	Gets the skewness of this distribution.
Matrix	getSubgenerator()
double	getVar()	Gets the variance of this distribution.
Matrix	initProb()	Property alias for getInitProb
double	mean()	Property alias for getMean
long	numberOfPhases()	Property alias for getNumberOfPhases
long	numPhases()	Property alias for getNumberOfPhases
MatrixCell	process()	Property alias for getProcess
double	rate()	Property alias for getRate
double[]	sample(int n)	Generates random samples from this distribution using default random generator.
double[]	sample(int n, Random random)	Generates random samples from this distribution using the specified random generator.
double	scv()	Property alias for getSCV
double	skewness()	Property alias for getSkewness
Matrix	subgenerator()	Property alias for getSubgenerator
double	var()	Property alias for getVar

Methods inherited from class jline.lang.processes.Markovian

acf, D, embedded, embeddedProb, evalCDF, evalLST, evalMeanT, evalVarT, getACF, getACF, getEmbedded, getEmbeddedProb, getIDC, getIDC, getIDI, getMoments, getMu, getPhi, getRepresentation, getVariance, idc, idi, moments, mu, phi, setMean, setProcess, setRate, variance

Methods inherited from class jline.lang.processes.Distribution

evalProbInterval, getFeatureName, getName, getNumParams, getNumParams, getParam, getParam, getParams, getSupport, hasParam, isContinuous, isDisabled, isDiscrete, isImmediate, isMarkovian, name, numParams, param, setNumParams, setParam, support, withDefect, withMassAtOrigin

Methods inherited from class java.lang.Object

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

Methods inherited from interface jline.lang.Copyable

copy

Constructor Details

PH

public PH(Matrix alpha,
 Matrix T)

Method Details

fit

public static PH fit(double mean,
 double scv,
 double skew)

Fits a PH from the mean, the squared coefficient of variation and the skewness.

The fit is the acyclic one of APH.fit(double, double, double), returned as a PH, as in the MATLAB and Python PH.fit, whose two-state search falls back to the acyclic fitter.

Parameters:

mean - mean

scv - squared coefficient of variation

skew - skewness

Returns:

the fitted PH

fitCentral

public static PH fitCentral(double mean,
 double var,
 double skew)

Fits a PH from the mean, the variance and the skewness.

Parameters:

mean - mean

var - variance

skew - skewness

Returns:

the fitted PH

fitMeanAndSCV

public static PH fitMeanAndSCV(double mean,
 double scv)

Fits a PH from the mean and the squared coefficient of variation, taking the minimum-skewness third moment of the acyclic class.

Parameters:

mean - mean

scv - squared coefficient of variation

Returns:

the fitted PH

fitRawMoments

public static PH fitRawMoments(double m1,
 double m2,
 double m3)

Fits a PH from the first three raw moments.

Parameters:

m1 - first moment

m2 - second moment

m3 - third moment

Returns:

the fitted PH

evalCDF

public double evalCDF(double t)

Evaluates the cumulative distribution function (CDF) at time t. For a PH distribution, CDF(t) = 1 - alpha * exp(T*t) * e where alpha is the initial probability vector, T is the subgenerator, and e is a vector of ones.

Overrides:

evalCDF in class Markovian

Parameters:

t - the time value

Returns:

the CDF value at time t

evalLST

public double evalLST(double s)

Description copied from class: Distribution

Evaluate the Laplace-Stieltjes Transform at s

Overrides:

evalLST in class Markovian

Parameters:

s - the Laplace domain variable

Returns:

the LST value at s

getInitProb

public Matrix getInitProb()

Description copied from class: Markovian

Gets the initial probability vector.

Overrides:

getInitProb in class Markovian

Returns:

the initial probabilities

getMean

public double getMean()

Description copied from class: Markovian

Gets the mean of this Markovian distribution.

Overrides:

getMean in class Markovian

Returns:

the mean value, or NaN if the process contains NaN values

getNumberOfPhases

public long getNumberOfPhases()

Description copied from class: Markovian

Gets the number of phases in this Markovian distribution.

Overrides:

getNumberOfPhases in class Markovian

Returns:

the number of phases

getProcess

public MatrixCell getProcess()

Description copied from class: Markovian

Gets the matrix representation of this Markovian process.

Overrides:

getProcess in class Markovian

Returns:

MatrixCell containing D0, D1, ... matrices

getRate

public double getRate()

Description copied from class: Distribution

Gets the rate of this distribution (inverse of mean).

Overrides:

getRate in class Markovian

Returns:

the rate value (1/mean)

getSCV

public double getSCV()

Description copied from class: Distribution

Gets the squared coefficient of variation (SCV) of this distribution. SCV = Var(X) / E[X]^2.

Overrides:

getSCV in class Markovian

Returns:

the squared coefficient of variation

getSkewness

public double getSkewness()

Description copied from class: Distribution

Gets the skewness of this distribution. Skewness measures the asymmetry of the probability distribution.

Overrides:

getSkewness in class Markovian

Returns:

the skewness value

getSubgenerator

public Matrix getSubgenerator()

Overrides:

getSubgenerator in class Markovian

getVar

public double getVar()

Description copied from class: Distribution

Gets the variance of this distribution. Computed as SCV * mean^2.

Overrides:

getVar in class Markovian

Returns:

the variance

sample

public double[] sample(int n)

Description copied from class: Distribution

Generates random samples from this distribution using default random generator.

Overrides:

sample in class Markovian

Parameters:

n - the number of samples to generate

Returns:

array of random samples

sample

public double[] sample(int n,
 Random random)

Description copied from class: Distribution

Generates random samples from this distribution using the specified random generator.

Overrides:

sample in class Markovian

Parameters:

n - the number of samples to generate

random - the random number generator to use

Returns:

array of random samples

mean

public double mean()

Property alias for getMean

Overrides:

mean in class Markovian

rate

public double rate()

Property alias for getRate

Overrides:

rate in class Markovian

scv

public double scv()

Property alias for getSCV

Overrides:

scv in class Markovian

skewness

public double skewness()

Property alias for getSkewness

Overrides:

skewness in class Markovian

var

public double var()

Property alias for getVar

Overrides:

var in class Markovian

initProb

public Matrix initProb()

Property alias for getInitProb

Overrides:

initProb in class Markovian

numberOfPhases

public long numberOfPhases()

Property alias for getNumberOfPhases

Overrides:

numberOfPhases in class Markovian

numPhases

public long numPhases()

Property alias for getNumberOfPhases

Overrides:

numPhases in class Markovian

process

public MatrixCell process()

Property alias for getProcess

Overrides:

process in class Markovian

subgenerator

public Matrix subgenerator()

Property alias for getSubgenerator

Overrides:

subgenerator in class Markovian