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TriangularDistribution Class

Triangular distribution.
Inheritance Hierarchy
SystemObject
  Accord.Statistics.DistributionsDistributionBase
    Accord.Statistics.Distributions.UnivariateUnivariateContinuousDistribution
      Accord.Statistics.Distributions.UnivariateTriangularDistribution

Namespace:  Accord.Statistics.Distributions.Univariate
Assembly:  Accord.Statistics (in Accord.Statistics.dll) Version: 3.7.0
Syntax
[SerializableAttribute]
public class TriangularDistribution : UnivariateContinuousDistribution, 
	ISampleableDistribution<double>, IDistribution<double>, IDistribution, 
	ICloneable, IRandomNumberGenerator<double>, IFittableDistribution<double, TriangularOptions>, 
	IFittable<double, TriangularOptions>, IFittable<double>, 
	IFittableDistribution<double>
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The TriangularDistribution type exposes the following members.

Constructors
  NameDescription
Public methodTriangularDistribution
Constructs a Triangular distribution with the given parameters a, b and c.
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Properties
  NameDescription
Public propertyEntropy
Gets the entropy for this distribution, defined as 0.5 + log((max-min)/2)).
(Overrides UnivariateContinuousDistributionEntropy.)
Public propertyMax
Gets the triangular parameter B (the maximum value).
Public propertyMean
Gets the mean for this distribution, defined as (a + b + c) / 3.
(Overrides UnivariateContinuousDistributionMean.)
Public propertyMedian
Gets the median for this distribution.
(Overrides UnivariateContinuousDistributionMedian.)
Public propertyMin
Gets the triangular parameter A (the minimum value).
Public propertyMode
Gets the mode for this distribution, also known as the triangular's c.
(Overrides UnivariateContinuousDistributionMode.)
Public propertyQuartiles
Gets the Quartiles for this distribution.
(Inherited from UnivariateContinuousDistribution.)
Public propertyStandardDeviation
Gets the Standard Deviation (the square root of the variance) for the current distribution.
(Inherited from UnivariateContinuousDistribution.)
Public propertySupport
Gets the distribution support, defined as (Min, Max).
(Overrides UnivariateContinuousDistributionSupport.)
Public propertyVariance
Gets the variance for this distribution, defined as (a² + b² + c² - ab - ac - bc) / 18.
(Overrides UnivariateContinuousDistributionVariance.)
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Methods
  NameDescription
Public methodClone
Creates a new object that is a copy of the current instance.
(Overrides DistributionBaseClone.)
Public methodComplementaryDistributionFunction
Gets the complementary cumulative distribution function (ccdf) for this distribution evaluated at point x. This function is also known as the Survival function.
(Inherited from UnivariateContinuousDistribution.)
Public methodCumulativeHazardFunction
Gets the cumulative hazard function for this distribution evaluated at point x.
(Inherited from UnivariateContinuousDistribution.)
Public methodDistributionFunction(Double)
Gets the cumulative distribution function (cdf) for this distribution evaluated at point x.
(Inherited from UnivariateContinuousDistribution.)
Public methodDistributionFunction(Double, Double)
Gets the cumulative distribution function (cdf) for this distribution in the semi-closed interval (a; b] given as P(a < X ≤ b).
(Inherited from UnivariateContinuousDistribution.)
Public methodEquals
Determines whether the specified object is equal to the current object.
(Inherited from Object.)
Protected methodFinalize
Allows an object to try to free resources and perform other cleanup operations before it is reclaimed by garbage collection.
(Inherited from Object.)
Public methodStatic memberFindMax
Finds the index of the last largest value in a set of observations.
Public methodStatic memberFindMin
Finds the index of the first smallest value in a set of observations.
Public methodFit(Double)
Fits the underlying distribution to a given set of observations.
(Inherited from UnivariateContinuousDistribution.)
Public methodFit(Double, IFittingOptions)
Fits the underlying distribution to a given set of observations.
(Inherited from UnivariateContinuousDistribution.)
Public methodFit(Double, Double)
Fits the underlying distribution to a given set of observations.
(Inherited from UnivariateContinuousDistribution.)
Public methodFit(Double, Int32)
Fits the underlying distribution to a given set of observations.
(Inherited from UnivariateContinuousDistribution.)
Public methodFit(Double, Double, IFittingOptions)
Fits the underlying distribution to a given set of observations.
(Overrides UnivariateContinuousDistributionFit(Double, Double, IFittingOptions).)
Public methodFit(Double, Double, TriangularOptions)
Fits the underlying distribution to a given set of observations.
Public methodFit(Double, Int32, IFittingOptions)
Fits the underlying distribution to a given set of observations.
(Overrides UnivariateContinuousDistributionFit(Double, Int32, IFittingOptions).)
Public methodFit(Double, Int32, TriangularOptions)
Fits the underlying distribution to a given set of observations.
Public methodGenerate
Generates a random observation from the current distribution.
(Inherited from UnivariateContinuousDistribution.)
Public methodGenerate(Random)
Generates a random observation from the current distribution.
(Overrides UnivariateContinuousDistributionGenerate(Random).)
Public methodGenerate(Int32)
Generates a random vector of observations from the current distribution.
(Inherited from UnivariateContinuousDistribution.)
Public methodGenerate(Int32, Double)
Generates a random vector of observations from the current distribution.
(Inherited from UnivariateContinuousDistribution.)
Public methodGenerate(Int32, Random)
Generates a random vector of observations from the current distribution.
(Inherited from UnivariateContinuousDistribution.)
Public methodGenerate(Int32, Double, Random)
Generates a random vector of observations from the current distribution.
(Overrides UnivariateContinuousDistributionGenerate(Int32, Double, Random).)
Public methodGetHashCode
Serves as the default hash function.
(Inherited from Object.)
Public methodStatic memberGetMax(Double, Double, Int32)
Gets the maximum value in a set of weighted observations.
Public methodStatic memberGetMax(Double, Int32, Int32)
Finds the index of the last largest value in a set of weighted observations.
Public methodStatic memberGetMin(Double, Double, Int32)
Gets the minimum value in a set of weighted observations.
Public methodStatic memberGetMin(Double, Int32, Int32)
Finds the index of the first smallest value in a set of weighted observations.
Public methodGetRange
Gets the distribution range within a given percentile.
(Inherited from UnivariateContinuousDistribution.)
Public methodGetType
Gets the Type of the current instance.
(Inherited from Object.)
Public methodHazardFunction
Gets the hazard function, also known as the failure rate or the conditional failure density function for this distribution evaluated at point x.
(Inherited from UnivariateContinuousDistribution.)
Protected methodInnerComplementaryDistributionFunction
Gets the complementary cumulative distribution function (ccdf) for this distribution evaluated at point x. This function is also known as the Survival function.
(Inherited from UnivariateContinuousDistribution.)
Protected methodInnerDistributionFunction
Gets the cumulative distribution function (cdf) for this distribution evaluated at point x.
(Overrides UnivariateContinuousDistributionInnerDistributionFunction(Double).)
Protected methodInnerInverseDistributionFunction
Gets the inverse of the cumulative distribution function (icdf) for this distribution evaluated at probability p. This function is also known as the Quantile function.
(Inherited from UnivariateContinuousDistribution.)
Protected methodInnerLogProbabilityDensityFunction
Gets the log-probability density function (pdf) for this distribution evaluated at point x.
(Inherited from UnivariateContinuousDistribution.)
Protected methodInnerProbabilityDensityFunction
Gets the probability density function (pdf) for this distribution evaluated at point x.
(Overrides UnivariateContinuousDistributionInnerProbabilityDensityFunction(Double).)
Public methodInverseDistributionFunction
Gets the inverse of the cumulative distribution function (icdf) for this distribution evaluated at probability p. This function is also known as the Quantile function.
(Inherited from UnivariateContinuousDistribution.)
Public methodLogCumulativeHazardFunction
Gets the log of the cumulative hazard function for this distribution evaluated at point x.
(Inherited from UnivariateContinuousDistribution.)
Public methodLogProbabilityDensityFunction
Gets the log-probability density function (pdf) for this distribution evaluated at point x.
(Inherited from UnivariateContinuousDistribution.)
Protected methodMemberwiseClone
Creates a shallow copy of the current Object.
(Inherited from Object.)
Public methodProbabilityDensityFunction
Gets the probability density function (pdf) for this distribution evaluated at point x.
(Inherited from UnivariateContinuousDistribution.)
Public methodQuantileDensityFunction
Gets the first derivative of the inverse distribution function (icdf) for this distribution evaluated at probability p.
(Inherited from UnivariateContinuousDistribution.)
Public methodToString
Returns a String that represents this instance.
(Inherited from DistributionBase.)
Public methodToString(IFormatProvider)
Returns a String that represents this instance.
(Inherited from DistributionBase.)
Public methodToString(String)
Returns a String that represents this instance.
(Inherited from DistributionBase.)
Public methodToString(String, IFormatProvider)
Returns a String that represents this instance.
(Overrides DistributionBaseToString(String, IFormatProvider).)
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Extension Methods
  NameDescription
Public Extension MethodHasMethod
Checks whether an object implements a method with the given name.
(Defined by ExtensionMethods.)
Public Extension MethodIsEqual
Compares two objects for equality, performing an elementwise comparison if the elements are vectors or matrices.
(Defined by Matrix.)
Public Extension MethodToT
Converts an object into another type, irrespective of whether the conversion can be done at compile time or not. This can be used to convert generic types to numeric types during runtime.
(Defined by ExtensionMethods.)
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Remarks

In probability theory and statistics, the triangular distribution is a continuous probability distribution with lower limit a, upper limit b and mode c, where a < b and a ≤ c ≤ b.

References:

Examples

This example shows how to create a Triangular distribution with minimum 1, maximum 6, and most common value 3.

// Create a new Triangular distribution (1, 3, 6).
var trig = new TriangularDistribution(a: 1, b: 6, c: 3);

double mean = trig.Mean;     // 3.3333333333333335
double median = trig.Median; // 3.2613872124741694
double mode = trig.Mode;     // 3.0
double var = trig.Variance;  // 1.0555555555555556

double cdf = trig.DistributionFunction(x: 2); // 0.10000000000000001
double pdf = trig.ProbabilityDensityFunction(x: 2); // 0.20000000000000001
double lpdf = trig.LogProbabilityDensityFunction(x: 2); // -1.6094379124341003

double ccdf = trig.ComplementaryDistributionFunction(x: 2); // 0.90000000000000002
double icdf = trig.InverseDistributionFunction(p: cdf); // 2.0000000655718773

double hf = trig.HazardFunction(x: 2); // 0.22222222222222224
double chf = trig.CumulativeHazardFunction(x: 2); // 0.10536051565782628

string str = trig.ToString(CultureInfo.InvariantCulture); // Triangular(x; a = 1, b = 6, c = 3)
See Also