TrapezoidalDistribution Class 
Namespace: Accord.Statistics.Distributions.Univariate
[SerializableAttribute] public class TrapezoidalDistribution : UnivariateContinuousDistribution
The TrapezoidalDistribution type exposes the following members.
Name  Description  

TrapezoidalDistribution(Double, Double, Double, Double) 
Creates a new trapezoidal distribution.
 
TrapezoidalDistribution(Double, Double, Double, Double, Double, Double) 
Creates a new trapezoidal distribution.
 
TrapezoidalDistribution(Double, Double, Double, Double, Double, Double, Double) 
Creates a new trapezoidal distribution.

Name  Description  

Entropy 
Not supported.
(Overrides UnivariateContinuousDistributionEntropy.)  
Mean 
Gets the mean for this distribution.
(Overrides UnivariateContinuousDistributionMean.)  
Median 
Gets the median for this distribution.
(Inherited from UnivariateContinuousDistribution.)  
Mode 
Gets the mode for this distribution.
(Inherited from UnivariateContinuousDistribution.)  
Quartiles 
Gets the Quartiles for this distribution.
(Inherited from UnivariateContinuousDistribution.)  
StandardDeviation 
Gets the Standard Deviation (the square root of
the variance) for the current distribution.
(Inherited from UnivariateContinuousDistribution.)  
Support 
Gets the support interval for this distribution.
(Overrides UnivariateContinuousDistributionSupport.)  
Variance 
Gets the variance for this distribution.
(Overrides UnivariateContinuousDistributionVariance.) 
Name  Description  

Clone 
Creates a new object that is a copy of the current instance.
(Overrides DistributionBaseClone.)  
ComplementaryDistributionFunction 
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.)  
CumulativeHazardFunction 
Gets the cumulative hazard function for this
distribution evaluated at point x.
(Inherited from UnivariateContinuousDistribution.)  
DistributionFunction(Double) 
Gets the cumulative distribution function (cdf) for
this distribution evaluated at point x.
(Inherited from UnivariateContinuousDistribution.)  
DistributionFunction(Double, Double) 
Gets the cumulative distribution function (cdf) for this
distribution in the semiclosed interval (a; b] given as
P(a < X ≤ b).
(Inherited from UnivariateContinuousDistribution.)  
Equals  Determines whether the specified object is equal to the current object. (Inherited from Object.)  
Finalize  Allows an object to try to free resources and perform other cleanup operations before it is reclaimed by garbage collection. (Inherited from Object.)  
Fit(Double) 
Fits the underlying distribution to a given set of observations.
(Inherited from UnivariateContinuousDistribution.)  
Fit(Double, IFittingOptions) 
Fits the underlying distribution to a given set of observations.
(Inherited from UnivariateContinuousDistribution.)  
Fit(Double, Double) 
Fits the underlying distribution to a given set of observations.
(Inherited from UnivariateContinuousDistribution.)  
Fit(Double, Int32) 
Fits the underlying distribution to a given set of observations.
(Inherited from UnivariateContinuousDistribution.)  
Fit(Double, Double, IFittingOptions) 
Fits the underlying distribution to a given set of observations.
(Inherited from UnivariateContinuousDistribution.)  
Fit(Double, Int32, IFittingOptions) 
Fits the underlying distribution to a given set of observations.
(Inherited from UnivariateContinuousDistribution.)  
Generate 
Generates a random observation from the current distribution.
(Inherited from UnivariateContinuousDistribution.)  
Generate(Int32) 
Generates a random vector of observations from the current distribution.
(Inherited from UnivariateContinuousDistribution.)  
Generate(Random) 
Generates a random observation from the current distribution.
(Inherited from UnivariateContinuousDistribution.)  
Generate(Int32, Double) 
Generates a random vector of observations from the current distribution.
(Inherited from UnivariateContinuousDistribution.)  
Generate(Int32, Random) 
Generates a random vector of observations from the current distribution.
(Inherited from UnivariateContinuousDistribution.)  
Generate(Int32, Double, Random) 
Generates a random vector of observations from the current distribution.
(Inherited from UnivariateContinuousDistribution.)  
GetHashCode  Serves as the default hash function. (Inherited from Object.)  
GetRange 
Gets the distribution range within a given percentile.
(Inherited from UnivariateContinuousDistribution.)  
GetType  Gets the Type of the current instance. (Inherited from Object.)  
HazardFunction 
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.)  
InnerComplementaryDistributionFunction 
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.)  
InnerDistributionFunction 
Gets the cumulative distribution function (cdf) for
this distribution evaluated at point x.
(Overrides UnivariateContinuousDistributionInnerDistributionFunction(Double).)  
InnerInverseDistributionFunction 
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.)  
InnerLogProbabilityDensityFunction 
Gets the logprobability density function (pdf) for
this distribution evaluated at point x.
(Inherited from UnivariateContinuousDistribution.)  
InnerProbabilityDensityFunction 
Gets the probability density function (pdf) for
this distribution evaluated at point x.
(Overrides UnivariateContinuousDistributionInnerProbabilityDensityFunction(Double).)  
InverseDistributionFunction 
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.)  
LogCumulativeHazardFunction 
Gets the log of the cumulative hazard function for this
distribution evaluated at point x.
(Inherited from UnivariateContinuousDistribution.)  
LogProbabilityDensityFunction 
Gets the logprobability density function (pdf) for
this distribution evaluated at point x.
(Inherited from UnivariateContinuousDistribution.)  
MemberwiseClone  Creates a shallow copy of the current Object. (Inherited from Object.)  
ProbabilityDensityFunction 
Gets the probability density function (pdf) for
this distribution evaluated at point x.
(Inherited from UnivariateContinuousDistribution.)  
QuantileDensityFunction 
Gets the first derivative of the
inverse distribution function (icdf) for this distribution evaluated
at probability p.
(Inherited from UnivariateContinuousDistribution.)  
ToString 
Returns a String that represents this instance.
(Inherited from DistributionBase.)  
ToString(IFormatProvider) 
Returns a String that represents this instance.
(Inherited from DistributionBase.)  
ToString(String) 
Returns a String that represents this instance.
(Inherited from DistributionBase.)  
ToString(String, IFormatProvider) 
Returns a String that represents this instance.
(Overrides DistributionBaseToString(String, IFormatProvider).) 
Name  Description  

HasMethod 
Checks whether an object implements a method with the given name.
(Defined by ExtensionMethods.)  
IsEqual 
Compares two objects for equality, performing an elementwise
comparison if the elements are vectors or matrices.
(Defined by Matrix.)  
To(Type)  Overloaded.
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.)  
ToT  Overloaded.
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.) 
Trapezoidal distributions have been used in many areas and studied under varying scopes, such as in the excellent work of (van Dorp and Kotz, 2003), risk analysis (Pouliquen, 1970) and (Powell and Wilson, 1997), fuzzy set theory (Chen and Hwang, 1992), applied phyisics, and biomedical applications (Flehinger and Kimmel, 1987).
Trapezoidal distributions are appropriate for modeling events that are comprised by three different stages: one growth stage, where probability grows up until a plateau is reached; a stability stage, where probability stays more or less the same; and a decline stage, where probability decreases until zero (van Dorp and Kotz, 2003).
References:
The following example shows how to create and test the main characteristics of a Trapezoidal distribution given its parameters:
// Create a new trapezoidal distribution with linear growth between // 0 and 2, stability between 2 and 8, and decrease between 8 and 10. // // // ++ // / \ // /   \ // /   \ // ++++ // ... 0 2 4 6 8 10 ... // var trapz = new TrapezoidalDistribution(a: 0, b: 2, c: 8, d: 10, n1: 1, n3: 1); double mean = trapz.Mean; // 2.25 double median = trapz.Median; // 3.0 double mode = trapz.Mode; // 3.1353457616424696 double var = trapz.Variance; // 17.986666666666665 double cdf = trapz.DistributionFunction(x: 1.4); // 0.13999999999999999 double pdf = trapz.ProbabilityDensityFunction(x: 1.4); // 0.10000000000000001 double lpdf = trapz.LogProbabilityDensityFunction(x: 1.4); // 2.3025850929940455 double ccdf = trapz.ComplementaryDistributionFunction(x: 1.4); // 0.85999999999999999 double icdf = trapz.InverseDistributionFunction(p: cdf); // 1.3999999999999997 double hf = trapz.HazardFunction(x: 1.4); // 0.11627906976744187 double chf = trapz.CumulativeHazardFunction(x: 1.4); // 0.15082288973458366 string str = trapz.ToString(CultureInfo.InvariantCulture); // Trapezoidal(x; a=0, b=2, c=8, d=10, n1=1, n3=1, α = 1)