Package org.apache.commons.statistics.distribution

Class TrapezoidalDistribution

java.lang.Object

org.apache.commons.statistics.distribution.AbstractContinuousDistribution

org.apache.commons.statistics.distribution.TrapezoidalDistribution

All Implemented Interfaces:

ContinuousDistribution

Direct Known Subclasses:

TrapezoidalDistribution.DelegatedTrapezoidalDistribution, TrapezoidalDistribution.RegularTrapezoidalDistribution

public abstract class TrapezoidalDistribution
extends AbstractContinuousDistribution

Implementation of the trapezoidal distribution.

The probability density function of \( X \) is:

\[ f(x; a, b, c, d) = \begin{cases} \frac{2}{d+c-a-b}\frac{x-a}{b-a} & \text{for } a\le x \lt b \\ \frac{2}{d+c-a-b} & \text{for } b\le x \lt c \\ \frac{2}{d+c-a-b}\frac{d-x}{d-c} & \text{for } c\le x \le d \end{cases} \]

for \( -\infty \lt a \le b \le c \le d \lt \infty \) and \( x \in [a, d] \).

Note the special cases:

• \( b = c \) is the triangular distribution
• \( a = b \) and \( c = d \) is the uniform distribution

See Also:

Trapezoidal distribution (Wikipedia)

Nested Class Summary

Nested Classes

Modifier and Type	Class	Description
private static class	TrapezoidalDistribution.DelegatedTrapezoidalDistribution	Specialisation of the trapezoidal distribution used when the distribution simplifies to an alternative distribution.
private static class	TrapezoidalDistribution.RegularTrapezoidalDistribution	Regular implementation of the trapezoidal distribution.
private static class	TrapezoidalDistribution.TriangularTrapezoidalDistribution	Specialisation of the trapezoidal distribution used when b == c.
private static class	TrapezoidalDistribution.UniformTrapezoidalDistribution	Specialisation of the trapezoidal distribution used when a == b and c == d.

Nested classes/interfaces inherited from interface org.apache.commons.statistics.distribution.ContinuousDistribution

ContinuousDistribution.Sampler

Field Summary

Fields

Modifier and Type	Field	Description
protected double	a	Lower limit of this distribution (inclusive).
protected double	b	Start of the trapezoid constant density.
protected double	c	End of the trapezoid constant density.
protected double	d	Upper limit of this distribution (inclusive).

Constructor Summary

Constructors

Constructor	Description
TrapezoidalDistribution(double a, double b, double c, double d)

Method Summary

Modifier and Type	Method	Description
double	getB()	Gets the start of the constant region of the density function.
double	getC()	Gets the end of the constant region of the density function.
abstract double	getMean()	Gets the mean of this distribution.
double	getSupportLowerBound()	Gets the lower bound of the support.
double	getSupportUpperBound()	Gets the upper bound of the support.
abstract double	getVariance()	Gets the variance of this distribution.
static TrapezoidalDistribution	of(double a, double b, double c, double d)	Creates a trapezoidal distribution.

Methods inherited from class org.apache.commons.statistics.distribution.AbstractContinuousDistribution

createSampler, getMedian, inverseCumulativeProbability, inverseSurvivalProbability, isSupportConnected, probability

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Methods inherited from interface org.apache.commons.statistics.distribution.ContinuousDistribution

cumulativeProbability, density, logDensity, survivalProbability

Field Detail

a

protected final double a

Lower limit of this distribution (inclusive).

b

protected final double b

Start of the trapezoid constant density.

c

protected final double c

End of the trapezoid constant density.

d

protected final double d

Upper limit of this distribution (inclusive).

Constructor Detail

TrapezoidalDistribution

TrapezoidalDistribution(double a,
                        double b,
                        double c,
                        double d)

Parameters:

a - Lower limit of this distribution (inclusive).

b - Start of the trapezoid constant density.

c - End of the trapezoid constant density.

d - Upper limit of this distribution (inclusive).

Method Detail

of

public static TrapezoidalDistribution of(double a,
                                         double b,
                                         double c,
                                         double d)

Creates a trapezoidal distribution.

The distribution density is represented as an up sloping line from a to b, constant from b to c, and then a down sloping line from c to d.

Parameters:

a - Lower limit of this distribution (inclusive).

b - Start of the trapezoid constant density (first shape parameter).

c - End of the trapezoid constant density (second shape parameter).

d - Upper limit of this distribution (inclusive).

Returns:

the distribution

Throws:

java.lang.IllegalArgumentException - if a >= d, if b < a, if c < b or if c > d.

getMean

public abstract double getMean()

Gets the mean of this distribution.

For lower limit \( a \), start of the density constant region \( b \), end of the density constant region \( c \) and upper limit \( d \), the mean is:

\[ \frac{1}{3(d+c-b-a)}\left(\frac{d^3-c^3}{d-c}-\frac{b^3-a^3}{b-a}\right) \]

Returns:

the mean.

getVariance

public abstract double getVariance()

Gets the variance of this distribution.

For lower limit \( a \), start of the density constant region \( b \), end of the density constant region \( c \) and upper limit \( d \), the variance is:

\[ \frac{1}{6(d+c-b-a)}\left(\frac{d^4-c^4}{d-c}-\frac{b^4-a^4}{b-a}\right) - \mu^2 \]

where \( \mu \) is the mean.

Returns:

the variance.

getB

public double getB()

Gets the start of the constant region of the density function.

This is the first shape parameter b of the distribution.

Returns:

the first shape parameter b

getC

public double getC()

Gets the end of the constant region of the density function.

This is the second shape parameter c of the distribution.

Returns:

the second shape parameter c

getSupportLowerBound

public double getSupportLowerBound()

Gets the lower bound of the support. It must return the same value as inverseCumulativeProbability(0), i.e. \( \inf \{ x \in \mathbb R : P(X \le x) \gt 0 \} \).

The lower bound of the support is equal to the lower limit parameter a of the distribution.

Returns:

the lower bound of the support.

getSupportUpperBound

public double getSupportUpperBound()

Gets the upper bound of the support. It must return the same value as inverseCumulativeProbability(1), i.e. \( \inf \{ x \in \mathbb R : P(X \le x) = 1 \} \).

The upper bound of the support is equal to the upper limit parameter d of the distribution.

Returns:

the upper bound of the support.