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Meta.Numerics.Statistics.Distributions.GumbelDistribution Class Reference

Represents a Gumbel distribution. More...

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

Public Member Functions

 GumbelDistribution ()
 Initializes a new standard Gumbel distribution. More...
 
 GumbelDistribution (double location, double scale)
 Initializes a new Gumbel distribution with the given parameters. 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 RightProbability (double x)
 Return the cumulative probability to the right of (above) the given point.
Parameters
xThe reference point.
Returns
The integrated probability 1-P(x1) to obtain a result above the reference point.
In survival analysis, the right probability function is commonly called the survival function, because it gives the fraction of the population remaining after the given time. 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 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 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 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 InverseRightProbability (double Q)
 Returns the point at which the right probability function attains the given value. 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 Interval Support [get]
 
double LocationParameter [get]
 Gets the location parameter of the distribution. More...
 
double ScaleParameter [get]
 Gets the scale parameter of the distribution. More...
 
override double Median [get]
 
override double Mean [get]
 
override double Variance [get]
 
override double StandardDeviation [get]
 
override double Skewness [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 Attributes

readonly double m
 
readonly double s
 

Detailed Description

Represents a Gumbel distribution.

Constructor & Destructor Documentation

Meta.Numerics.Statistics.Distributions.GumbelDistribution.GumbelDistribution ( )
inline

Initializes a new standard Gumbel distribution.

Meta.Numerics.Statistics.Distributions.GumbelDistribution.GumbelDistribution ( double  location,
double  scale 
)
inline

Initializes a new Gumbel distribution with the given parameters.

Parameters
locationThe location parameter.
scaleThe scale parameter, which must be positive.
Exceptions
ArgumentOutOfRangeExceptionscale is negative or zero.

Member Function Documentation

override double Meta.Numerics.Statistics.Distributions.GumbelDistribution.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.GumbelDistribution.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.GumbelDistribution.RightProbability ( double  x)
inlinevirtual

Return the cumulative probability to the right of (above) the given point.

Parameters
xThe reference point.
Returns
The integrated probability 1-P(x1) to obtain a result above the reference point.
In survival analysis, the right probability function is commonly called the survival function, because it gives the fraction of the population remaining after the given time.

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

References Meta.Numerics.MoreMath.ExpMinusOne().

override double Meta.Numerics.Statistics.Distributions.GumbelDistribution.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.

override double Meta.Numerics.Statistics.Distributions.GumbelDistribution.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.

override double Meta.Numerics.Statistics.Distributions.GumbelDistribution.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.

override double Meta.Numerics.Statistics.Distributions.GumbelDistribution.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.Factorial(), Meta.Numerics.MoreMath.Pow(), and Meta.Numerics.Functions.AdvancedMath.RiemannZeta().

Member Data Documentation

readonly double Meta.Numerics.Statistics.Distributions.GumbelDistribution.m
private
readonly double Meta.Numerics.Statistics.Distributions.GumbelDistribution.s
private

Property Documentation

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

double Meta.Numerics.Statistics.Distributions.GumbelDistribution.LocationParameter
get

Gets the location parameter of the distribution.

double Meta.Numerics.Statistics.Distributions.GumbelDistribution.ScaleParameter
get

Gets the scale parameter of the distribution.

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

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

override double Meta.Numerics.Statistics.Distributions.GumbelDistribution.Variance
get

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

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


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