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Meta.Numerics.Statistics.Distributions.TriangularDistribution Class Reference

Represents a triangular distribution. More...

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

Public Member Functions

 TriangularDistribution (double a, double b, double c)
 Initializes a new triangular 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 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 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...
 
- 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...
 
- Public Member Functions inherited from Meta.Numerics.Statistics.Distributions.UnivariateDistribution
virtual double Cumulant (int r)
 Computes a cumulant of the distribution. More...
 

Properties

override double Mean [get]
 
override double Variance [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 LeftTriangleArea (double x)
 
double RightTrigangleArea (double x)
 
double MomentAboutMode (int n)
 

Private Attributes

double a
 
double b
 
double c
 
double ab
 
double bc
 
double ac
 
double h
 

Detailed Description

Represents a triangular distribution.

Like a uniform distribution, a triangular distribution is confined to a finite interval. Unlike a uniform distribution, a triangular distribution is not uniform across the interval.

Triangular distributions are often used in project planning, where a maximum, minimum, and most likely value for some quantity is known or supposed.

Constructor & Destructor Documentation

Meta.Numerics.Statistics.Distributions.TriangularDistribution.TriangularDistribution ( double  a,
double  b,
double  c 
)
inline

Initializes a new triangular distribution.

Parameters
aOne inflection point of the distribution.
bA second inflection point of the distribution.
cA third inflection point of the distribution.

Member Function Documentation

override double Meta.Numerics.Statistics.Distributions.TriangularDistribution.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.TriangularDistribution.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.TriangularDistribution.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.

double Meta.Numerics.Statistics.Distributions.TriangularDistribution.LeftTriangleArea ( double  x)
inlineprivate
double Meta.Numerics.Statistics.Distributions.TriangularDistribution.RightTrigangleArea ( double  x)
inlineprivate
override double Meta.Numerics.Statistics.Distributions.TriangularDistribution.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.

double Meta.Numerics.Statistics.Distributions.TriangularDistribution.MomentAboutMode ( int  n)
inlineprivate
override double Meta.Numerics.Statistics.Distributions.TriangularDistribution.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.

References Meta.Numerics.Functions.AdvancedIntegerMath.BinomialCoefficient().

override double Meta.Numerics.Statistics.Distributions.TriangularDistribution.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.Functions.AdvancedIntegerMath.BinomialCoefficient().

Member Data Documentation

double Meta.Numerics.Statistics.Distributions.TriangularDistribution.a
private
double Meta.Numerics.Statistics.Distributions.TriangularDistribution.b
private
double Meta.Numerics.Statistics.Distributions.TriangularDistribution.c
private
double Meta.Numerics.Statistics.Distributions.TriangularDistribution.ab
private
double Meta.Numerics.Statistics.Distributions.TriangularDistribution.bc
private
double Meta.Numerics.Statistics.Distributions.TriangularDistribution.ac
private
double Meta.Numerics.Statistics.Distributions.TriangularDistribution.h
private

Property Documentation

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

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

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


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