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

Interface IProbabilityMassFunction

All Superinterfaces:

IProbabilityFunction

All Known Implementing Classes:

ProbabilityMassFunctionImpl

public interface IProbabilityMassFunction
extends IProbabilityFunction

A probability mass function (abbreviated pmf) gives the probability that a discrete random variable is exactly equal to some value. A probability mass function differs from a probability density function in that the values of the latter, defined only for continuous random variables, are not probabilities; rather, its integral over a set of possible values of the random variable is a probability. Note that the operations defined here are not suitable to add and multiply random numbers in general (e.g. in the DependencySolver). They are defined per-value and are required for internal computations (e.g. Fourier Transformation).

Method Summary

Modifier and Type	Method	Description
IProbabilityMassFunction	add(IProbabilityMassFunction pmf)	Adds the probabilities of two probability mass functions (pmf) on a 'per value' basis. h(x) = f(x) + g(x) (f = this, g = parameter pmf) For the addition, the domains of both pmfs have to be equal.
IProbabilityMassFunction	div(IProbabilityMassFunction pmf)	Divides the probabilities of two probability mass functions (pmf) on a 'per value' basis. h(x) = f(x) / g(x) (f = this, g = parameter pmf) For the division, the domains of both pmfs have to be equal.
Object	drawSample()	Generates a random number of the probability function's domain, whose distribution is defined by the probability function.
IProbabilityMassFunction	getCumulativeFunction()	returns the cumulative probability function associated with this probability function.
IProbabilityMassFunction	getFourierTramsform()	Computes the Fourier transform of the probability mass function.
IProbabilityMassFunction	getInverseFourierTransform()	Computes the inverse Fourier transform of the probability mass function.
List<ISample>	getSamples()	List of samples describing the pmf.
boolean	haveSameDomain(IProbabilityMassFunction pmf)	Check whether the two PMFs have compatible domains.
IProbabilityMassFunction	mult(IProbabilityMassFunction pmf)	Multiplies the probabilities of two probability mass functions (pmf) on a 'per value' basis. h(x) = f(x) * g(x) (f = this, g = parameter pmf) For the multiplication, the domains of both pmfs have to be equal.
IProbabilityMassFunction	scale(double scalar)	Scales the probabilities of a probability mass functions (pmf) on a 'per value' basis. h(x) = a * f(x) (f = this, a = parameter scalar)
void	setSamples(List<ISample> samples)	List of samples describing the pmf.
IProbabilityMassFunction	shiftDomain(double scalar)	Shifts each value of the PMF by the given scalar (i.e., adds the given scalar to each value).
IProbabilityMassFunction	stretchDomain(double scalar)	Stretches the domain of the PMF by the given scalar (i.e, multiplies each value with the given scalar).
IProbabilityMassFunction	sub(IProbabilityMassFunction pmf)	Substracts the probabilities of two probability mass functions (pmf) on a 'per value' basis. h(x) = f(x) - g(x) (f = this, g = parameter pmf) For the substraction, the domains of both pmfs have to be equal.

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

checkConstrains, getArithmeticMeanValue, getMedian, getPercentile, getProbabilitySum, getUnit, hasOrderedDomain, isInFrequencyDomain, isInTimeDomain

Method Detail

drawSample

Object drawSample()

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

Returns:

A sample of the PMF's domain.

add

IProbabilityMassFunction add(IProbabilityMassFunction pmf)
                      throws DifferentDomainsException

Adds the probabilities of two probability mass functions (pmf) on a 'per value' basis.
h(x) = f(x) + g(x) (f = this, g = parameter pmf)
For the addition, the domains of both pmfs have to be equal. This means that

* the value objects of the pmf's samples have to be of the same class and * for each value object of the samples in function f (this) there is exactly one equal value object in the samples of function g (pmf) and vice versa. Here, equal means that Object.equal(...) returns true for both objects.
If the domain of both functions are not equal, a DifferentDomainsException is thrown.

Parameters:

pmf - Function to add.

Returns:

A new pmf that contains the sum of both.

Throws:

DifferentDomainsException - if the domains of both function differ.

sub

IProbabilityMassFunction sub(IProbabilityMassFunction pmf)
                      throws DifferentDomainsException

Substracts the probabilities of two probability mass functions (pmf) on a 'per value' basis.
h(x) = f(x) - g(x) (f = this, g = parameter pmf)
For the substraction, the domains of both pmfs have to be equal. This means that

* the value objects of the pmf's samples have to be of the same class and * for each value object of the samples in function f (this) there is exactly one equal value object in the samples of function g (pmf) and vice versa. Here, equal means that Object.equal(...) returns true for both objects.
If the domain of both functions are not equal, a DifferentDomainsException is thrown.

Parameters:

pmf - Function to substract.

Returns:

A new pmf that contains the difference of both.

Throws:

DifferentDomainsException - if the domains of both function differ.

mult

IProbabilityMassFunction mult(IProbabilityMassFunction pmf)
                       throws DifferentDomainsException

Multiplies the probabilities of two probability mass functions (pmf) on a 'per value' basis.
h(x) = f(x) * g(x) (f = this, g = parameter pmf)
For the multiplication, the domains of both pmfs have to be equal. This means that

* the value objects of the pmf's samples have to be of the same class and * for each value object of the samples in function f (this) there is exactly one equal value object in the samples of function g (pmf) and vice versa. Here, equal means that Object.equal(...) returns true for both objects.
If the domain of both functions are not equal, a DifferentDomainsException is thrown.

Parameters:

pmf - Function to multiply with.

Returns:

A new pmf that contains the product of both.

Throws:

DifferentDomainsException - if the domains of both function differ.

div

IProbabilityMassFunction div(IProbabilityMassFunction pmf)
                      throws DifferentDomainsException

Divides the probabilities of two probability mass functions (pmf) on a 'per value' basis.
h(x) = f(x) / g(x) (f = this, g = parameter pmf)
For the division, the domains of both pmfs have to be equal. This means that

* the value objects of the pmf's samples have to be of the same class and * for each value object of the samples in function f (this) there is exactly one equal value object in the samples of function g (pmf) and vice versa. Here, equal means that Object.equal(...) returns true for both objects.
If the domain of both functions are not equal, a DifferentDomainsException is thrown.

Parameters:

pmf - Function to divide by.

Returns:

A new pmf that contains the fraction of both.

Throws:

DifferentDomainsException - if the domains of both function differ.

scale

IProbabilityMassFunction scale(double scalar)

Scales the probabilities of a probability mass functions (pmf) on a 'per value' basis.
h(x) = a * f(x) (f = this, a = parameter scalar)

Parameters:

scalar - the value to scale the probabilities.

Returns:

A new pmf that contains the scaled probabilities.

shiftDomain

IProbabilityMassFunction shiftDomain(double scalar)
                              throws DomainNotNumbersException

Shifts each value of the PMF by the given scalar (i.e., adds the given scalar to each value). If the scalar is larger than zero, the PMF gets shifted to the right, otherwise it gets shifted to the left.

Parameters:

scalar -

Returns:

Throws:

DomainNotNumbersException

stretchDomain

IProbabilityMassFunction stretchDomain(double scalar)
                                throws DomainNotNumbersException

Stretches the domain of the PMF by the given scalar (i.e, multiplies each value with the given scalar). If the scalar is larger than 1, the PMF gets stretched. If the scalar is between zero and 1, the PMF gets compressed.

Parameters:

scalar -

Returns:

Throws:

DomainNotNumbersException

getFourierTramsform

IProbabilityMassFunction getFourierTramsform()
                                      throws FunctionNotInTimeDomainException

Computes the Fourier transform of the probability mass function. Note, that you should only use this function if you really know what you are doing, as this doesn't make sense in many cases for pmfs!

Can only be applied if 'isInTimeDomain()' is true, otherwise a FunctionNotInTimeDomainException is thrown.

Returns:

Fourier transform of pmf (in time domain).

Throws:

FunctionNotInTimeDomainException

getInverseFourierTransform

IProbabilityMassFunction getInverseFourierTransform()
                                             throws FunctionNotInFrequencyDomainException

Computes the inverse Fourier transform of the probability mass function. Note, that you should only use this function if you really know what you are doing, as this doesn't make sense in many cases for pmfs!

Can only be applied if 'isInFrequencyDomain()' is true, otherwise a FunctionNotInFrequencyDomainException is thrown.

Returns:

Fourier transform of pmf (in time domain).

Throws:

FunctionNotInFrequencyDomainException

getSamples

List<ISample> getSamples()

List of samples describing the pmf. They associate a value (x axis) with a probability (y axis). In case 'hasOrderedDomain' is true, they are sorted. Note: The function returns only a copy of the sample list.

Returns:

A Copy of the list of (ordered) samples describing the pmf.

setSamples

void setSamples(List<ISample> samples)

List of samples describing the pmf. They associate a value (x axis) with a probability (y axis). In case the values can be ordered, they will be sorted. Note: The sum of all probabilities has to be one!

Parameters:

samples - New list of samples describing the pmf.

Throws:

ProbabilitySumNotOneException - Thrown if the sum of the samples probabilities is not one.

haveSameDomain

boolean haveSameDomain(IProbabilityMassFunction pmf)

Check whether the two PMFs have compatible domains. Integers are casted to doubles if one of the PMFs is a DoublePMF. TODO: check whether this behaviour is fine for the rest of the tools, because other classes may expect exactly the same type.

Parameters:

pmf -

Returns:

getCumulativeFunction

IProbabilityMassFunction getCumulativeFunction()

returns the cumulative probability function associated with this probability function.

Returns:

the computed cumulative probability function.