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Meta.Numerics.Statistics.Distributions.UniformDistribution Class Reference

Represents a uniform distribution over an interval. More...

+ Inheritance diagram for Meta.Numerics.Statistics.Distributions.UniformDistribution:
+ Collaboration diagram for Meta.Numerics.Statistics.Distributions.UniformDistribution:

Public Member Functions

 UniformDistribution (Interval range)
 Initializes a new uniform distribution on the given interval. More...
 
 UniformDistribution ()
 Initializes a new standard uniform distribution. More...
 
override double ProbabilityDensity (double x)
 Returns the probability density at the given point.
Parameters
xThe reference point.
Returns
The probability density p(x).
The probability density function (PDF) gives the relative probability of obtaining different values. More...
 
override double LeftProbability (double x)
 Returns the cumulative probability to the left of (below) the given point.
Parameters
xThe reference point.
Returns
The integrated probability to obtain a result below the reference point.
The left probability function is commonly called the cumulative distribution function (CDF). More...
 
override double InverseLeftProbability (double P)
 Returns the point at which the cumulative distribution function attains a given value.
Parameters
PThe left cumulative probability P, which must lie between 0 and 1.
Returns
The value x at which LeftProbability equals P.
The inverse left probability is commonly called the quantile function. Given a quantile, it tells which variable value is the lower border of that quantile. More...
 
override double InverseRightProbability (double Q)
 Returns the point at which the right probability function attains the given value.
Parameters
QThe right cumulative probability, which must lie between 0 and 1.
Returns
The value x for which RightProbability equals Q.
More...
 
override double Moment (int r)
 Computes a raw moment of the distribution.
Parameters
rThe order of the moment to compute.
Returns
The rth raw moment of the distribution.
See also
Moment
More...
 
override double MomentAboutMean (int r)
 Computes a central moment of the distribution.
Parameters
rThe order of the moment to compute.
Returns
The rth central moment of the distribution.
See also
Moment
More...
 
override double Cumulant (int r)
 Computes a cumulant of the distribution.
Parameters
rThe index of the cumulant to compute.
Returns
The rth cumulant of the distribution.
More...
 
- Public Member Functions inherited from Meta.Numerics.Statistics.Distributions.Distribution
virtual double RightProbability (double x)
 Return the cumulative probability to the right of (above) the given point. More...
 
virtual double ExpectationValue (Func< double, double > f)
 Computes the expectation value of the given function. More...
 
virtual double GetRandomValue (Random rng)
 Returns a random value. More...
 

Properties

override double Mean [get]
 
override double StandardDeviation [get]
 
override double Skewness [get]
 
override double ExcessKurtosis [get]
 
override double Median [get]
 
override Interval Support [get]
 
- Properties inherited from Meta.Numerics.Statistics.Distributions.Distribution
virtual double Median [get]
 Gets the median of the distribution. More...
 
virtual Interval Support [get]
 Gets the interval over which the distribution is nonvanishing. More...
 
- Properties inherited from Meta.Numerics.Statistics.Distributions.UnivariateDistribution
virtual double Mean [get]
 Gets the mean of the distribution. More...
 
virtual double Variance [get]
 Gets the variance of the distribution. More...
 
virtual double StandardDeviation [get]
 Gets the standard deviation of the distribution. More...
 
virtual double Skewness [get]
 Gets the skewness of the distribution. More...
 
virtual double ExcessKurtosis [get]
 Gets the excess kurtosis of the distribution. More...
 

Private Member Functions

double InverseProbability (double P, double Q)
 

Static Private Member Functions

static double DifferenceOfPowers (double a, double b, int n)
 
static double SumOfPowers (double a, double b, int n)
 
static double[] Powers (double a, int n)
 

Private Attributes

readonly Interval range
 

Detailed Description

Represents a uniform distribution over an interval.

Constructor & Destructor Documentation

Meta.Numerics.Statistics.Distributions.UniformDistribution.UniformDistribution ( Interval  range)
inline

Initializes a new uniform distribution on the given interval.

Parameters
rangeThe range of the distribution.
Meta.Numerics.Statistics.Distributions.UniformDistribution.UniformDistribution ( )
inline

Initializes a new standard uniform distribution.

A standard uniform distribution is uniform on the interval [0,1].

References Meta.Numerics.Interval.FromEndpoints().

Member Function Documentation

override double Meta.Numerics.Statistics.Distributions.UniformDistribution.ProbabilityDensity ( double  x)
inlinevirtual

Returns the probability density at the given point.

Parameters
xThe reference point.
Returns
The probability density p(x).
The probability density function (PDF) gives the relative probability of obtaining different values.

Implements Meta.Numerics.Statistics.Distributions.Distribution.

override double Meta.Numerics.Statistics.Distributions.UniformDistribution.LeftProbability ( double  x)
inlinevirtual

Returns the cumulative probability to the left of (below) the given point.

Parameters
xThe reference point.
Returns
The integrated probability to obtain a result below the reference point.
The left probability function is commonly called the cumulative distribution function (CDF).

Reimplemented from Meta.Numerics.Statistics.Distributions.Distribution.

override double Meta.Numerics.Statistics.Distributions.UniformDistribution.InverseLeftProbability ( double  P)
inlinevirtual

Returns the point at which the cumulative distribution function attains a given value.

Parameters
PThe left cumulative probability P, which must lie between 0 and 1.
Returns
The value x at which LeftProbability equals P.
The inverse left probability is commonly called the quantile function. Given a quantile, it tells which variable value is the lower border of that quantile.

Reimplemented from Meta.Numerics.Statistics.Distributions.Distribution.

Referenced by Test.DataSetTest.CreateDataSet().

override double Meta.Numerics.Statistics.Distributions.UniformDistribution.InverseRightProbability ( double  Q)
inlinevirtual

Returns the point at which the right probability function attains the given value.

Parameters
QThe right cumulative probability, which must lie between 0 and 1.
Returns
The value x for which RightProbability equals Q.

Reimplemented from Meta.Numerics.Statistics.Distributions.Distribution.

double Meta.Numerics.Statistics.Distributions.UniformDistribution.InverseProbability ( double  P,
double  Q 
)
inlineprivate
override double Meta.Numerics.Statistics.Distributions.UniformDistribution.Moment ( int  r)
inlinevirtual

Computes a raw moment of the distribution.

Parameters
rThe order of the moment to compute.
Returns
The rth raw moment of the distribution.
See also
Moment

Reimplemented from Meta.Numerics.Statistics.Distributions.Distribution.

static double Meta.Numerics.Statistics.Distributions.UniformDistribution.DifferenceOfPowers ( double  a,
double  b,
int  n 
)
inlinestaticprivate
static double Meta.Numerics.Statistics.Distributions.UniformDistribution.SumOfPowers ( double  a,
double  b,
int  n 
)
inlinestaticprivate
static double [] Meta.Numerics.Statistics.Distributions.UniformDistribution.Powers ( double  a,
int  n 
)
inlinestaticprivate
override double Meta.Numerics.Statistics.Distributions.UniformDistribution.MomentAboutMean ( int  r)
inlinevirtual

Computes a central moment of the distribution.

Parameters
rThe order of the moment to compute.
Returns
The rth central moment of the distribution.
See also
Moment

Reimplemented from Meta.Numerics.Statistics.Distributions.Distribution.

References Meta.Numerics.MoreMath.Pow().

override double Meta.Numerics.Statistics.Distributions.UniformDistribution.Cumulant ( int  r)
inlinevirtual

Computes a cumulant of the distribution.

Parameters
rThe index of the cumulant to compute.
Returns
The rth cumulant of the distribution.

Reimplemented from Meta.Numerics.Statistics.Distributions.UnivariateDistribution.

References Meta.Numerics.Functions.AdvancedIntegerMath.BernoulliNumber(), and Meta.Numerics.MoreMath.Pow().

Member Data Documentation

readonly Interval Meta.Numerics.Statistics.Distributions.UniformDistribution.range
private

Property Documentation

override double Meta.Numerics.Statistics.Distributions.UniformDistribution.Mean
get

override double Meta.Numerics.Statistics.Distributions.UniformDistribution.StandardDeviation
get

override double Meta.Numerics.Statistics.Distributions.UniformDistribution.Skewness
get

override double Meta.Numerics.Statistics.Distributions.UniformDistribution.ExcessKurtosis
get

override double Meta.Numerics.Statistics.Distributions.UniformDistribution.Median
get

override Interval Meta.Numerics.Statistics.Distributions.UniformDistribution.Support
get


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