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

Class GammaDistribution

java.lang.Object

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

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

All Implemented Interfaces:

IContinousPDF, IGammaDistribution, IProbabilityDensityFunction, IProbabilityFunction

Direct Known Subclasses:

GammaDistributionFromMoments

public class GammaDistribution
extends AbstractContinousPDF
implements IGammaDistribution

See Also:

• IGammaDistribution

Field Summary

Fields inherited from class de.uka.ipd.sdq.probfunction.math.apache.impl.AbstractContinousPDF

internalFunction, sampleDrawer

Constructor Summary

Constructors

Modifier	Constructor	Description
	GammaDistribution(double alpha, double theta, IRandomGenerator rng)	Constructs a GammaDist object with parameters alpha and theta.
protected	GammaDistribution(IRandomGenerator rng)

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).
void	checkConstrains()	checks whether the following constraints are fulfilled : the sum of all probabilities is one.
double	density(double x)	Returns f(x), the density evaluated at x, as defined in umontreal.iro.lecuyer.probdist.ContinousDistribution#density(double)
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	getAlpha()	Shape parameter
double	getArithmeticMeanValue()	For a probability function, whose domain is integer or real the arithmetic mean - the sum of all measurements divided by the number of observations in the data set - is returned.
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	getLowerDomainBorder()	Returns the smallest values of the domain.
Object	getMedian()	A median is a number dividing the higher half of a sample, a population, or a probability distribution from the lower half.
Object	getPercentile(int p)	In descriptive statistics, the 'p'th percentile is a scale value for a data series equal to the p/100 quantile.
double	getStandardDeviation()
double	getTheta()	Scale parameter beta
double	getVariance()
double	getXinf()	Returns xb such that the probability density is 0 everywhere outside the interval [xa, xb],
double	getXsup()	Returns xa such that the probability density is 0 everywhere outside the interval [xa, xb]
double	greaterThan(IProbabilityDensityFunction pdf)	Computes the probability that the random variable specified by this PDF is greater than the random variable specified by pdf.
boolean	hasOrderedDomain()	If the domain of the probability functions is ordered, true is returned; false otherwise.
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.
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 de.uka.ipd.sdq.probfunction.math.apache.impl.AbstractContinousPDF

cdf, drawSample, getCoefficientOfVariance, getProbabilitySum, getUnit, inverseF, isInFrequencyDomain, isInTimeDomain

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.IContinousPDF

cdf, getCoefficientOfVariance, inverseF

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

drawSample

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

getProbabilitySum, getUnit, isInFrequencyDomain, isInTimeDomain

Constructor Details

GammaDistribution

public GammaDistribution(double alpha,
 double theta,
 IRandomGenerator rng)

Constructs a GammaDist object with parameters alpha and theta.

Parameters:

alpha - shape parameter

theta - scale parameter = 1 / rate parameter

GammaDistribution

protected GammaDistribution(IRandomGenerator rng)

Method Details

density

public double density(double x)

Description copied from class: AbstractContinousPDF

Returns f(x), the density evaluated at x, as defined in umontreal.iro.lecuyer.probdist.ContinousDistribution#density(double)

Specified by:

density in interface IContinousPDF

Overrides:

density in class AbstractContinousPDF

Returns:

F(x)

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

Overrides:

add in class AbstractContinousPDF

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

Overrides:

div in class AbstractContinousPDF

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

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

Overrides:

getFourierTransform in class AbstractContinousPDF

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

Overrides:

getInverseFourierTransform in class AbstractContinousPDF

Returns:

inverse fourier transform of the PDF (in time domain)

Throws:

FunctionNotInFrequencyDomainException

getLowerDomainBorder

public double getLowerDomainBorder()

Description copied from interface: IProbabilityDensityFunction

Returns the smallest values of the domain. At the moment this will be zero. However, future implementations might allow arbitrary values here.

Specified by:

getLowerDomainBorder in interface IProbabilityDensityFunction

Returns:

Smallest value of the domain.

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

Overrides:

greaterThan in class AbstractContinousPDF

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

Overrides:

lessThan in class AbstractContinousPDF

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

Overrides:

mult in class AbstractContinousPDF

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

Overrides:

probabilisticEquals in class AbstractContinousPDF

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

Overrides:

scale in class AbstractContinousPDF

Parameters:

scalar - a, value to scale with.

Returns:

The scaled function a*f(x)

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

Overrides:

sub in class AbstractContinousPDF

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

Overrides:

checkConstrains in class AbstractContinousPDF

Throws:

NegativeDistanceException

ProbabilitySumNotOneException

FunctionNotInTimeDomainException

UnitNotSetException

UnitNameNotSetException

InvalidSampleValueException

getMedian

public Object getMedian()
                 throws UnorderedDomainException

Description copied from interface: IProbabilityFunction

A median is a number dividing the higher half of a sample, a population, or a probability distribution from the lower half. The median of a finite list of numbers can be found by arranging all the observations from lowest value to highest value and picking the middle one.

Specified by:

getMedian in interface IProbabilityFunction

Returns:

Object that is the border for the median.

Throws:

UnorderedDomainException

getPercentile

public Object getPercentile(int p)
                     throws IndexOutOfBoundsException,
UnorderedDomainException

Description copied from interface: IProbabilityFunction

In descriptive statistics, the 'p'th percentile is a scale value for a data series equal to the p/100 quantile. Thus:
* The 1st percentile cuts off lowest 1% of data
* The 98th percentile cuts off lowest 98% of data
* The 25th percentile is the first quartile
* The 50th percentile is the median.
One definition is that the pth percentile of n ordered values is obtained by first calculating the rank k = p(n+1)/100, rounded to the nearest integer and then taking the value that corresponds to that rank.

Specified by:

getPercentile in interface IProbabilityFunction

Parameters:

p - sets the percentile which shall be computed. p must take values between 0 and 100.

Returns:

Object that is the border for the 'p'th percentile.

Throws:

IndexOutOfBoundsException

UnorderedDomainException

hasOrderedDomain

public boolean hasOrderedDomain()

Description copied from interface: IProbabilityFunction

If the domain of the probability functions is ordered, true is returned; false otherwise.

Specified by:

hasOrderedDomain in interface IProbabilityFunction

Returns:

True, if the domain is ordered.

getAlpha

public double getAlpha()

Shape parameter

Specified by:

getAlpha in interface IGammaDistribution

getTheta

public double getTheta()

Scale parameter beta

Specified by:

getTheta in interface IGammaDistribution

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

Overrides:

getCumulativeFunction in class AbstractContinousPDF

Returns:

the computed cumulative probability function.

Throws:

FunctionNotInTimeDomainException

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

Overrides:

shiftDomain in class AbstractContinousPDF

Returns:

Throws:

DomainNotNumbersException

getVariance

public double getVariance()

Specified by:

getVariance in interface IContinousPDF

Overrides:

getVariance in class AbstractContinousPDF

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

Overrides:

stretchDomain in class AbstractContinousPDF

Returns:

getStandardDeviation

public double getStandardDeviation()

Specified by:

getStandardDeviation in interface IContinousPDF

getXinf

public double getXinf()

Description copied from interface: IContinousPDF

Returns xb such that the probability density is 0 everywhere outside the interval [xa, xb],

Specified by:

getXinf in interface IContinousPDF

Returns:

lower limit of support

getXsup

public double getXsup()

Description copied from interface: IContinousPDF

Returns xa such that the probability density is 0 everywhere outside the interval [xa, xb]

Specified by:

getXsup in interface IContinousPDF

Returns:

upper limit of support

getArithmeticMeanValue

public double getArithmeticMeanValue()
                              throws DomainNotNumbersException,
FunctionNotInTimeDomainException

Description copied from interface: IProbabilityFunction

For a probability function, whose domain is integer or real the arithmetic mean - the sum of all measurements divided by the number of observations in the data set - is returned.

Specified by:

getArithmeticMeanValue in interface IProbabilityFunction

Returns:

The arithmetic mean.

Throws:

DomainNotNumbersException

FunctionNotInTimeDomainException