Package de.uka.ipd.sdq.probfunction.math.apache.impl

Class AbstractDiscretePDF

java.lang.Object

de.uka.ipd.sdq.probfunction.math.apache.impl.AbstractDiscretePDF

All Implemented Interfaces:

IDiscretePDF, IProbabilityDensityFunction, IProbabilityFunction

Direct Known Subclasses:

BinomialDistribution, PoissonDistribution, UniformIntDistribution

public abstract class AbstractDiscretePDF
extends Object
implements IDiscretePDF

Field Summary

Fields

Modifier and Type	Field	Description
protected org.apache.commons.math.distribution.AbstractIntegerDistribution	internalFunction
protected IRandomGenerator	sampleDrawer

Constructor Summary

Constructors

Constructor	Description
AbstractDiscretePDF()

Method Summary

Modifier and Type	Method	Description
IProbabilityDensityFunction	add(IProbabilityDensityFunction pdf)	Adds two ProbabilityDensityFunctions on a "per value" basis: h(x) = f(x) + g(x) An addition can only be performed if both functions are in the same domain (frequency or time).
double	cdf(double x)	Returns the distribution function F(x) as defined in umontreal.iro.lecuyer.probdist.Distribution#cdf(double)
double	cdf(int x)	Returns the distribution function F(x) as defined in umontreal.iro.lecuyer.probdist.Distribution#cdf(double)
void	checkConstrains()	checks whether the following constraints are fulfilled : the sum of all probabilities is one.
IProbabilityDensityFunction	div(IProbabilityDensityFunction pdf)	Divides two ProbabilityDensityFunctions on a "per value" basis: h(x) = f(x) / g(x) A division can only be performed if both functions are in the same domain (frequency or time).
double	drawSample()	Generates a random number of the probability function's domain, whose distribution is defined by the probability function.
double	getCoefficientOfVariance()
IProbabilityDensityFunction	getCumulativeFunction()	returns the cumulative probability function associated with this probability function.
IProbabilityDensityFunction	getFourierTransform()	Computes the fourier transform of the probability density function.
IProbabilityDensityFunction	getInverseFourierTransform()	Computes the inverse fourier transform of the probability density function.
double	getProbabilitySum()	Computes the sum of all probabilities specified in the function.
IUnit	getUnit()	Returns the unit of the probability functions domain.
double	getVariance()
double	greaterThan(IProbabilityDensityFunction pdf)	Computes the probability that the random variable specified by this PDF is greater than the random variable specified by pdf.
int	inverseF(double u)	Computes and returns the inverse distribution function x = F^{-1}(u).
boolean	isInFrequencyDomain()	True, if the probability density function is in the frequency domain (frequency domain graph shows how much of the signal lies within each given frequency band over a range of frequencies).
boolean	isInTimeDomain()	True, if the probability density function is the time domain (a time domain graph shows how a signal changes over time).
double	lessThan(IProbabilityDensityFunction pdf)	Computes the probability that the random variable specified by this PDF is less than the random variable specified by pdf.
IProbabilityDensityFunction	mult(IProbabilityDensityFunction pdf)	Multiplies two ProbabilityDensityFunctions on a "per value" basis: h(x) = f(x) * g(x) A multiplication can only be performed if both functions are in the same domain (frequency or time).
double	probabilisticEquals(IProbabilityDensityFunction pdf)	Computes the probability that two random variables characterised by the given PDFs are equal.
double	probability(int x)	Returns f(x), the probability evaluated at x
IProbabilityDensityFunction	scale(double scalar)	Scales a ProbabilityDensityFunctions on a "per value" basis: h(x) = a * f(x)
IProbabilityDensityFunction	shiftDomain(double scalar)	Shifts the domain values of the PDF by the given scalar
IProbabilityDensityFunction	stretchDomain(double scalar)	Stretches the domain values of the PDF.
IProbabilityDensityFunction	sub(IProbabilityDensityFunction pdf)	Subtracts two ProbabilityDensityFunctions on a "per value" basis: h(x) = f(x) - g(x) A substraction can only be performed if both functions are in the same domain (frequency or time).

Methods inherited from class java.lang.Object

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

Methods inherited from interface de.uka.ipd.sdq.probfunction.math.IDiscretePDF

getMean, getStandardDeviation, getXinf, getXsup

Methods inherited from interface de.uka.ipd.sdq.probfunction.math.IProbabilityDensityFunction

getLowerDomainBorder

Methods inherited from interface de.uka.ipd.sdq.probfunction.math.IProbabilityFunction

getArithmeticMeanValue, getMedian, getPercentile, hasOrderedDomain

Field Detail

internalFunction

protected org.apache.commons.math.distribution.AbstractIntegerDistribution internalFunction

sampleDrawer

protected IRandomGenerator sampleDrawer

Constructor Detail

AbstractDiscretePDF

public AbstractDiscretePDF()

Method Detail

cdf

public double cdf(int x)

Returns the distribution function F(x) as defined in umontreal.iro.lecuyer.probdist.Distribution#cdf(double)

Specified by:

cdf in interface IDiscretePDF

Parameters:

x -

Returns:

F(x)

getCoefficientOfVariance

public double getCoefficientOfVariance()

getVariance

public double getVariance()

Specified by:

getVariance in interface IDiscretePDF

getProbabilitySum

public double getProbabilitySum()

Description copied from interface: IProbabilityFunction

Computes the sum of all probabilities specified in the function. For pdfs this is the area under the graph; for pmfs the sum of all probabilities.

Specified by:

getProbabilitySum in interface IProbabilityFunction

Returns:

Sum of all probabilities in the function.

probability

public double probability(int x)

Description copied from interface: IDiscretePDF

Returns f(x), the probability evaluated at x

Specified by:

probability in interface IDiscretePDF

Returns:

f(x)

isInFrequencyDomain

public boolean isInFrequencyDomain()

Description copied from interface: IProbabilityFunction

True, if the probability density function is in the frequency domain (frequency domain graph shows how much of the signal lies within each given frequency band over a range of frequencies). This means it is the result of a Fourier transformation.

Specified by:

isInFrequencyDomain in interface IProbabilityFunction

Returns:

True, if in frequency domain, false otherwise.

isInTimeDomain

public boolean isInTimeDomain()

Description copied from interface: IProbabilityFunction

True, if the probability density function is the time domain (a time domain graph shows how a signal changes over time). This means that it is not a result of a Fourier transform.

Specified by:

isInTimeDomain in interface IProbabilityFunction

Returns:

True, if in time domain; false otherwise.

cdf

public double cdf(double x)

Returns the distribution function F(x) as defined in umontreal.iro.lecuyer.probdist.Distribution#cdf(double)

Parameters:

x -

Returns:

F(x)

drawSample

public double drawSample()

Description copied from interface: IProbabilityDensityFunction

Generates a random number of the probability function's domain, whose distribution is defined by the probability function.

Specified by:

drawSample in interface IProbabilityDensityFunction

Returns:

A sample of the PDF's domain.

inverseF

public int inverseF(double u)

Computes and returns the inverse distribution function x = F^{-1}(u). This can be used to get the quantiles of the distribution. Pass 0.9 to get the x value of this function for which this.cdf(x) = 0.9 holds. Uses the implementation of the concrete function in the umontreal.iro.lecuyer.probdist package.

Specified by:

inverseF in interface IDiscretePDF

Parameters:

u - - value in the interval [0, 1] for which the inverse distribution function is evaluated

Returns:

the inverse distribution function evaluated at u

getUnit

public IUnit getUnit()

Description copied from interface: IProbabilityFunction

Returns the unit of the probability functions domain.

Specified by:

getUnit in interface IProbabilityFunction

Returns:

unit of the probability functions domain.

add

public IProbabilityDensityFunction add(IProbabilityDensityFunction pdf)
                                throws FunctionsInDifferenDomainsException,
                                       UnknownPDFTypeException,
                                       IncompatibleUnitsException

Description copied from interface: IProbabilityDensityFunction

Adds two ProbabilityDensityFunctions on a "per value" basis:
h(x) = f(x) + g(x)
An addition can only be performed if both functions are in the same domain (frequency or time). If not a FunctionsInDifferenDomainsException is thrown.

Specified by:

add in interface IProbabilityDensityFunction

Parameters:

pdf - g(x), probability density function to add.

Returns:

The sum of this function (f(x)) and pdf (g(x))

Throws:

FunctionsInDifferenDomainsException - Thrown if both functions are in different domains.

UnknownPDFTypeException - Thrown if one of the function is of an unknown type (not SamplePDf or BoxedPDF).

IncompatibleUnitsException - Thrown if both functions have units that do not match.

div

public IProbabilityDensityFunction div(IProbabilityDensityFunction pdf)
                                throws FunctionsInDifferenDomainsException,
                                       UnknownPDFTypeException,
                                       IncompatibleUnitsException

Description copied from interface: IProbabilityDensityFunction

Divides two ProbabilityDensityFunctions on a "per value" basis:
h(x) = f(x) / g(x)
A division can only be performed if both functions are in the same domain (frequency or time). If not a FunctionsInDifferenDomainsException is thrown.

Specified by:

div in interface IProbabilityDensityFunction

Parameters:

pdf - g(x), probability density function to divide by.

Returns:

The fraction of this function (f(x)) and pdf (g(x))

Throws:

FunctionsInDifferenDomainsException

UnknownPDFTypeException

IncompatibleUnitsException

getCumulativeFunction

public IProbabilityDensityFunction getCumulativeFunction()
                                                  throws FunctionNotInTimeDomainException

Description copied from interface: IProbabilityDensityFunction

returns the cumulative probability function associated with this probability function.

Specified by:

getCumulativeFunction in interface IProbabilityDensityFunction

Returns:

the computed cumulative probability function.

Throws:

FunctionNotInTimeDomainException

getFourierTransform

public IProbabilityDensityFunction getFourierTransform()
                                                throws FunctionNotInTimeDomainException

Description copied from interface: IProbabilityDensityFunction

Computes the fourier transform of the probability density function. Can only be applied if 'isInTimeDomain()' is true, otherwise a FunctionNotInTimeDomain exception is thrown.

Specified by:

getFourierTransform in interface IProbabilityDensityFunction

Returns:

fourier transform of the PDF (in frequency domain)

Throws:

FunctionNotInTimeDomainException

getInverseFourierTransform

public IProbabilityDensityFunction getInverseFourierTransform()
                                                       throws FunctionNotInFrequencyDomainException

Description copied from interface: IProbabilityDensityFunction

Computes the inverse fourier transform of the probability density function. Can only be applied if 'isInFrequencyDomain()' is true, otherwise a FunctionNotInFrequencyDomainException is thrown.

Specified by:

getInverseFourierTransform in interface IProbabilityDensityFunction

Returns:

inverse fourier transform of the PDF (in time domain)

Throws:

FunctionNotInFrequencyDomainException

greaterThan

public double greaterThan(IProbabilityDensityFunction pdf)
                   throws ProbabilityFunctionException

Description copied from interface: IProbabilityDensityFunction

Computes the probability that the random variable specified by this PDF is greater than the random variable specified by pdf. Note that the randomvariables have to be independent.

Specified by:

greaterThan in interface IProbabilityDensityFunction

Parameters:

pdf - PDF to compare to.

Returns:

Probability X_this > X_pdf

Throws:

ProbabilityFunctionException

lessThan

public double lessThan(IProbabilityDensityFunction pdf)
                throws ProbabilityFunctionException

Description copied from interface: IProbabilityDensityFunction

Computes the probability that the random variable specified by this PDF is less than the random variable specified by pdf. Note that the randomvariables have to be independent.

Specified by:

lessThan in interface IProbabilityDensityFunction

Parameters:

pdf - PDF to compare to.

Returns:

Probability X_this < X_pdf

Throws:

ProbabilityFunctionException

mult

public IProbabilityDensityFunction mult(IProbabilityDensityFunction pdf)
                                 throws FunctionsInDifferenDomainsException,
                                        UnknownPDFTypeException,
                                        IncompatibleUnitsException

Description copied from interface: IProbabilityDensityFunction

Multiplies two ProbabilityDensityFunctions on a "per value" basis:
h(x) = f(x) * g(x)
A multiplication can only be performed if both functions are in the same domain (frequency or time). If not a FunctionsInDifferenDomainsException is thrown.

Specified by:

mult in interface IProbabilityDensityFunction

Parameters:

pdf - g(x), probability density function to multiply with.

Returns:

The product of this function (f(x)) and pdf (g(x))

Throws:

FunctionsInDifferenDomainsException - Thrown if both functions are in different domains.

UnknownPDFTypeException - Thrown if one of the function is of an unknown type (not SamplePDf or BoxedPDF).

IncompatibleUnitsException - Thrown if both functions have units that do not match.

probabilisticEquals

public double probabilisticEquals(IProbabilityDensityFunction pdf)
                           throws ProbabilityFunctionException

Description copied from interface: IProbabilityDensityFunction

Computes the probability that two random variables characterised by the given PDFs are equal. Note that the randomvariables have to be independent.

Specified by:

probabilisticEquals in interface IProbabilityDensityFunction

Parameters:

pdf - PDF to compare to.

Returns:

Probability that the two random variables characterised by the PDFs are equal.

Throws:

ProbabilityFunctionException

scale

public IProbabilityDensityFunction scale(double scalar)

Description copied from interface: IProbabilityDensityFunction

Scales a ProbabilityDensityFunctions on a "per value" basis:
h(x) = a * f(x)

Specified by:

scale in interface IProbabilityDensityFunction

Parameters:

scalar - a, value to scale with.

Returns:

The scaled function a*f(x)

shiftDomain

public IProbabilityDensityFunction shiftDomain(double scalar)
                                        throws DomainNotNumbersException

Description copied from interface: IProbabilityDensityFunction

Shifts the domain values of the PDF by the given scalar

Specified by:

shiftDomain in interface IProbabilityDensityFunction

Returns:

Throws:

DomainNotNumbersException

stretchDomain

public IProbabilityDensityFunction stretchDomain(double scalar)

Description copied from interface: IProbabilityDensityFunction

Stretches the domain values of the PDF. This is equivalent to the multiplication of the specified random variable by the given scalar.

Specified by:

stretchDomain in interface IProbabilityDensityFunction

Returns:

sub

public IProbabilityDensityFunction sub(IProbabilityDensityFunction pdf)
                                throws FunctionsInDifferenDomainsException,
                                       UnknownPDFTypeException,
                                       IncompatibleUnitsException

Description copied from interface: IProbabilityDensityFunction

Subtracts two ProbabilityDensityFunctions on a "per value" basis:
h(x) = f(x) - g(x)
A substraction can only be performed if both functions are in the same domain (frequency or time). If not a FunctionsInDifferenDomainsException is thrown.

Specified by:

sub in interface IProbabilityDensityFunction

Parameters:

pdf - g(x), probability density function to substract.

Returns:

The difference of this function (f(x)) and pdf (g(x))

Throws:

FunctionsInDifferenDomainsException - Thrown if both functions are in different domains.

UnknownPDFTypeException - Thrown if one of the function is of an unknown type (not SamplePDf or BoxedPDF).

IncompatibleUnitsException - Thrown if both functions have units that do not match.

checkConstrains

public void checkConstrains()
                     throws NegativeDistanceException,
                            ProbabilitySumNotOneException,
                            FunctionNotInTimeDomainException,
                            UnitNotSetException,
                            UnitNameNotSetException,
                            InvalidSampleValueException

Description copied from interface: IProbabilityFunction

checks whether the following constraints are fulfilled : the sum of all probabilities is one. all values are greater or equal 0.

Specified by:

checkConstrains in interface IProbabilityFunction

Throws:

NegativeDistanceException

ProbabilitySumNotOneException

FunctionNotInTimeDomainException

UnitNotSetException

UnitNameNotSetException

InvalidSampleValueException