Package org.drip.measure.distribution

Class R1ContinuousUniform

java.lang.Object

org.drip.measure.distribution.R1Continuous

org.drip.measure.distribution.R1ContinuousUniform

Direct Known Subclasses:

R1ContinuousUniformPiecewiseDisplaced, R1ContinuousUniformPiecewiseLinear

public class R1ContinuousUniform
extends R1Continuous

R1ContinuousUniform implements the Univariate R¹ Uniform, i. e., Lebesgue Distribution. It implements the Incremental, the Cumulative, and the Inverse Cumulative Distribution Densities. It provides the following Functionality:

• Construct a Standard (0, 1) R¹ Univariate Uniform Distribution
• R1ContinuousUniform Constructor
• Retrieve the Left Support
• Retrieve the Right Support
• Indicate if the specified x Value stays inside the Support
• Lay out the Support of the PDF Range
• Compute the cumulative under the distribution to the given value
• Compute the Incremental under the Distribution between the 2 variates
• Compute the inverse cumulative under the distribution corresponding to the given value
• Compute the Density under the Distribution at the given Variate
• Retrieve the Mean of the Distribution
• Retrieve the Variance of the Distribution
• Generate a Random Variable corresponding to the Distribution
• Retrieve the Univariate Weighted Histogram

Module	Computational Core Module
Library	Numerical Analysis Library
Project	Rd Continuous/Discrete Probability Measures
Package	R1 and Rd Continuous Random Measure

Author:

Lakshmi Krishnamurthy

Constructor Summary

Constructors

Constructor	Description
R1ContinuousUniform(double leftSupport, double rightSupport)	R1ContinuousUniform Constructor

Method Summary

Modifier and Type	Method	Description
double	cumulative(double x)	Compute the cumulative under the distribution to the given value
double	density(double x)	Compute the Density under the Distribution at the given Variate
Array2D	histogram()	Retrieve the Univariate Weighted Histogram
double	incremental(double xLeft, double xRight)	Compute the Incremental under the Distribution between the 2 variates
double	invCumulative(double p)	Compute the inverse cumulative under the distribution corresponding to the given value
double	leftSupport()	Retrieve the Left Support
double	mean()	Retrieve the Mean of the Distribution
double	random()	Generate a Random Variable corresponding to the Distribution
double	rightSupport()	Retrieve the Right Support
static R1ContinuousUniform	Standard()	Construct a Standard (0, 1) R1 Uniform Distribution
double[]	support()	Lay out the Support of the PDF Range
boolean	supported(double x)	Indicate if the specified x Value stays inside the Support
double	variance()	Retrieve the Variance of the Distribution

Methods inherited from class org.drip.measure.distribution.R1Continuous

bPOE, centralMoment, cvar, differentialEntropy, excessKurtosis, expectedShortfall, fisherInformation, iqr, kullbackLeiblerDivergence, median, mode, nonCentralMoment, populationCentralMeasures, probabilityGeneratingFunction, quadratureEstimator, quantile, randomArray, skewness, tukeyAnomaly, tukeyCriterion

Methods inherited from class java.lang.Object

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

Constructor Details

R1ContinuousUniform

public R1ContinuousUniform(double leftSupport,
double rightSupport)
                    throws java.lang.Exception

R1ContinuousUniform Constructor

Parameters:

leftSupport - The Left Support

rightSupport - The Right Support

Throws:

java.lang.Exception - Thrown if the Inputs are Invalid

Method Details

Standard

public static final R1ContinuousUniform Standard()

Construct a Standard (0, 1) R¹ Uniform Distribution

Returns:

Standard (0, 1) R¹ Uniform Distribution

leftSupport

public double leftSupport()

Retrieve the Left Support

Returns:

The Left Support

rightSupport

public double rightSupport()

Retrieve the Right Support

Returns:

The Right Support

supported

public boolean supported(double x)

Indicate if the specified x Value stays inside the Support

Overrides:

supported in class R1Continuous

Parameters:

x - X

Returns:

The Value stays in Support

support

public double[] support()

Lay out the Support of the PDF Range

Specified by:

support in class R1Continuous

Returns:

Support of the PDF Range

cumulative

public double cumulative(double x)
                  throws java.lang.Exception

Compute the cumulative under the distribution to the given value

Overrides:

cumulative in class R1Continuous

Parameters:

x - Variate to which the cumulative is to be computed

Returns:

The cumulative

Throws:

java.lang.Exception - Thrown if the inputs are invalid

incremental

public double incremental(double xLeft,
double xRight)
                   throws java.lang.Exception

Compute the Incremental under the Distribution between the 2 variates

Overrides:

incremental in class R1Continuous

Parameters:

xLeft - Left Variate to which the cumulative is to be computed

xRight - Right Variate to which the cumulative is to be computed

Returns:

The Incremental under the Distribution between the 2 variates

Throws:

java.lang.Exception - Thrown if the inputs are invalid

invCumulative

public double invCumulative(double p)
                     throws java.lang.Exception

Compute the inverse cumulative under the distribution corresponding to the given value

Overrides:

invCumulative in class R1Continuous

Parameters:

p - Value corresponding to which the inverse cumulative is to be computed

Returns:

The inverse cumulative

Throws:

java.lang.Exception - Thrown if the Input is invalid

density

public double density(double x)
               throws java.lang.Exception

Compute the Density under the Distribution at the given Variate

Specified by:

density in class R1Continuous

Parameters:

x - Variate at which the Density needs to be computed

Returns:

The Density

Throws:

java.lang.Exception - Thrown if the input is invalid

mean

public double mean()

Retrieve the Mean of the Distribution

Overrides:

mean in class R1Continuous

Returns:

The Mean of the Distribution

Throws:

java.lang.Exception - Thrown if the Mean cannot be estimated

variance

public double variance()

Retrieve the Variance of the Distribution

Overrides:

variance in class R1Continuous

Returns:

The Variance of the Distribution

Throws:

java.lang.Exception - Thrown if the Variance cannot be estimated

random

public double random()

Generate a Random Variable corresponding to the Distribution

Overrides:

random in class R1Continuous

Returns:

Random Variable corresponding to the Distribution

Throws:

java.lang.Exception - Thrown if the Random Instance cannot be estimated

histogram

public Array2D histogram()

Retrieve the Univariate Weighted Histogram

Overrides:

histogram in class R1Continuous

Returns:

The Univariate Weighted Histogram