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diracDistribution Class Reference

The Dirac distribution concentrated at some point. More...

#include <diracDistribution.h>

Inheritance diagram for diracDistribution:
discreteDistribution Distribution

Public Member Functions

 diracDistribution (double val)
 Unique constructor for the Dirac distribution from its value. More...
 
double value (int)
 Read accessor to the value of the Dirac distribution. More...
 
double getProba (double value)
 Calculation of the mean. Returns the value since it is pre-computed. More...
 
double mean ()
 computing the mathematical expectation or mean More...
 
double rate ()
 computing the "rate", defined as the inverse of the mean More...
 
double moment (int order)
 Computing the moments of the distribution. More...
 
double variance ()
 Variance of the Dirac distribution. Reimplemented to return always 0. More...
 
double laplace (double s)
 computing the Laplace transform of the distribution at real point More...
 
double dLaplace (double s)
 computing the derivative of the Laplace transform at real points More...
 
double cdf (double x)
 computing the cumulative distribution function at some real point x. This is the probability that the random variable is less or equal to x. More...
 
bool hasMoment (int order)
 test for the existence of moments of any order More...
 
diracDistributionrescale (double factor)
 rescaling a distribution by some real factor. Not all distributions allow this for any real factor. If the operation fails, or if the factor is 1.0, a copy of the distribution should be returned (not by using the copy() function). More...
 
diracDistributioncopy ()
 copying a distribution. Typically implemented as rescale(1.0). More...
 
double sample ()
 drawing a (pseudo)random value according to the distribution. More...
 
void iidSample (int n, double *s)
 Sampling of i.i.d. values in a table. Reimplemented in order to avoid useless function calls. More...
 
std::string toString ()
 an utility to convert the distribution into a string. More...
 
void write (FILE *out, int mode)
 an utility to write the distribution to some file, according to some format. More...
 
- Public Member Functions inherited from discreteDistribution
 discreteDistribution (int sz, double *vals, double *probas)
 Constructor for a general discrete distribution from arrays. The arrays are ***copied***, not taken as pointer. The mean is calculated at creation. More...
 
 discreteDistribution (int sz, char *name)
 Constructor for a general discrete distribution from a file. The file is assumed to contain only the probas. The values are arbitrarily chosen between 0 and sz-1. The mean is calculated at creation. More...
 
 ~discreteDistribution ()
 Destructor for a general discrete distribution. The convention is that internal arrays for values and probas are freed at this moment. If they are useful for something else, they sould be copied. More...
 
double getProbaByIndex (int i)
 Read accessor for the elements of the probas array. This is a pseudo-accessor since it performs additional checks. More...
 
double getProba (double value)
 Computes the probability of a particular value. The tolerance VALUE_TOLERANCE is applied to match values. More...
 
double getValue (int i)
 Read accessor for the values. This is a pseudo-accessor since it performs additional checks. More...
 
int nbVals ()
 Read accessor to the number of values in the distribution. More...
 
bool setProba (int i, double v)
 Write accessor for the probas. This is a pseudo-accessor since it performs additional checks. More...
 
double mean ()
 Calculation of the mean. Returns the value since it is pre-computed. More...
 
double rate ()
 Calculation of the rate, which is the inverse of the mean. If the mean is 0, the value INFINITE_RATE is returned. More...
 
double moment (int order)
 Computing the moments of the distribution. More...
 
double laplace (double s)
 computing the Laplace transform of the distribution at real point More...
 
double dLaplace (double s)
 computing the derivative of the Laplace transform at real points More...
 
double cdf (double x)
 Computation of the cumulative density function at some real point x. More...
 
bool hasMoment (int order)
 Test of existence of a moment. These distributions always have one. More...
 
discreteDistributionrescale (double factor)
 rescaling a distribution by some real factor. Not all distributions allow this for any real factor. If the operation fails, or if the factor is 1.0, a copy of the distribution should be returned (not by using the copy() function). More...
 
discreteDistributioncopy ()
 copying a distribution. Typically implemented as rescale(1.0). More...
 
double sample ()
 Sampling from the law This is the straightforward, non optimized, linear-time algorithm. More...
 
double distanceL2 (discreteDistribution *d)
 Computes the L2 distance between two distributions. In case of incompatible or infinite sizes, a negative number is returned. More...
 
double distanceL1 (discreteDistribution *d)
 Computes the L1 distance between this distribution and another one. In case of incompatible or infinite sizes, a negative number is returned. More...
 
double distanceLinfinity (discreteDistribution *d)
 Computes the L-infinity distance between two distributions. In case of incompatible or infinite sizes, a negative number is returned. More...
 
std::string toString ()
 Printing a representation of the law into a string. More...
 
void write (FILE *out, int mode)
 Printing a representation of the law. More...
 
- Public Member Functions inherited from Distribution
virtual ~Distribution ()
 Standard destructor. More...
 
std::string name ()
 Read accessor to the type name of the distribution. More...
 
double variance ()
 Computing the variance of the random variable: the second moment minus the square of the first moment. Variance is the square of the coefficient of variation. The Distribution class offers a default implementation. More...
 
double ccdf (double x)
 computing the complementary cumulative distributon function (or tail) at some real point x. This is the probability that the random variable is strictly larger than x. The Distribution class offers a default implementation. More...
 
void iidSample (int n, double *s)
 drawing an i.i.d. sample from the distribution. The result is returned in an array (that must have been already allocated) passed as a parameter. The Distribution class offers the default implementation with repeated call to sample(). More...
 
virtual double distanceL1 (Distribution *d)
 Computing generally the L1 distance between distributions. More...
 
virtual bool hasProperty (std::string pro)
 Property test function. Current properties are: More...
 
void fprint ()
 write on stdout with NORMAL_PRINT_MODE More...
 

Additional Inherited Members

- Static Public Member Functions inherited from Distribution
static double u_0_1 (void)
 
static double exponential (double mean)
 
- Protected Member Functions inherited from discreteDistribution
 discreteDistribution (int sz)
 Constructor for a general discrete distribution from its size. Arrays are created to this size but not initialized. DANGEROUS to use since methods cannot check whether these arrays are correct or not. Use reserved to sub-types such as diracDistribution. More...
 
- Protected Attributes inherited from discreteDistribution
int _nbVals
 
double * _values
 
double * _probas
 
- Protected Attributes inherited from Distribution
std::string _name
 
double _mean
 
- Static Protected Attributes inherited from Distribution
static const double VALUE_TOLERANCE = 1.0e-8
 

Detailed Description

The Dirac distribution concentrated at some point.

Constructor & Destructor Documentation

diracDistribution::diracDistribution ( double  val)

Unique constructor for the Dirac distribution from its value.

Parameters
valthe value at which the distribution is concentrated

Constructor for a Dirac distribution. The mean is calculated at creation.

Author
Alain Jean-Marie
Parameters
valthe value of the deterministic law
Returns
an object of type diracDistribution

Member Function Documentation

double diracDistribution::cdf ( double  x)
virtual

computing the cumulative distribution function at some real point x. This is the probability that the random variable is less or equal to x.

Parameters
xthe value at which to compute the cdf
Returns
the value of the cdf

Computation of the cumulative density function at some real point x

Author
Alain Jean-Marie
Parameters
xvalue at which the CDF is computed
Returns
CDF(x)

Implements Distribution.

diracDistribution * diracDistribution::copy ( )
virtual

copying a distribution. Typically implemented as rescale(1.0).

See also
rescale(double)
Returns
a copy of the distribution

Implements Distribution.

double diracDistribution::dLaplace ( double  s)
virtual

computing the derivative of the Laplace transform at real points

Parameters
sthe value at which to compute
Returns
the value of the derivative of the Laplace transform

Computation of the derivative of the Laplace transform at some real point s

Author
Alain Jean-Marie
Parameters
svalue at which the derivative is computed
Returns
d LT(s)/ds

Implements Distribution.

double diracDistribution::getProba ( double  value)

Calculation of the mean. Returns the value since it is pre-computed.

Author
Alain Jean-Marie
Returns
the mathematical expectation of the distribution
bool diracDistribution::hasMoment ( int  order)
virtual

test for the existence of moments of any order

Parameters
orderthe order of the moment to be tested
Returns
true if the moment exists, false otherwise

Test of existence of a moment. These distributions always have one.

Author
Alain Jean-Marie
Parameters
orderorder of the moment
Returns
true

Implements Distribution.

void diracDistribution::iidSample ( int  n,
double *  s 
)

Sampling of i.i.d. values in a table. Reimplemented in order to avoid useless function calls.

Parameters
nthe number of values to sample
san array to be filled with the sample
double diracDistribution::laplace ( double  s)
virtual

computing the Laplace transform of the distribution at real point

Parameters
sthe value at which to compute
Returns
the value of the Laplace transform

Computation of the Laplace transform at some real point s

Author
Alain Jean-Marie
Parameters
svalue at which the derivative is computed
Returns
LT(s)

Implements Distribution.

double diracDistribution::mean ( )
virtual

computing the mathematical expectation or mean

Returns
the mean

Calculation of the mean. Returns the value since it is pre-computed

Author
Alain Jean-Marie
Returns
the mathematical expectation of the distribution

Implements Distribution.

double diracDistribution::moment ( int  order)
virtual

Computing the moments of the distribution.

Parameters
orderthe order of the moment to be computed
Returns
the moment

Implements Distribution.

double diracDistribution::rate ( )
virtual

computing the "rate", defined as the inverse of the mean

Returns
the rate

Calculation of the rate, which is the inverse of the mean

Author
Alain Jean-Marie
Returns
the rate

Implements Distribution.

diracDistribution * diracDistribution::rescale ( double  factor)
virtual

rescaling a distribution by some real factor. Not all distributions allow this for any real factor. If the operation fails, or if the factor is 1.0, a copy of the distribution should be returned (not by using the copy() function).

See also
copy()
Parameters
factorthe real factor to be used
Returns
a new distribution object

Implements Distribution.

double diracDistribution::sample ( )
virtual

drawing a (pseudo)random value according to the distribution.

Returns
a sample

Implements Distribution.

std::string diracDistribution::toString ( )
virtual

an utility to convert the distribution into a string.

Returns
the string representing the distribution.

Printing a representation of the law into a string

Author
Alain Jean-Marie
Returns
a string

Implements Distribution.

double diracDistribution::value ( int  )
inline

Read accessor to the value of the Dirac distribution.

Returns
the value of the distribution
double diracDistribution::variance ( )

Variance of the Dirac distribution. Reimplemented to return always 0.

void diracDistribution::write ( FILE *  out,
int  mode 
)
virtual

an utility to write the distribution to some file, according to some format.

Parameters
outthe file descriptor of the file
modea code for the format to be used

Implements Distribution.


The documentation for this class was generated from the following files: