Package org.drip.measure.gaussian

Class R1UnivariateNormal

java.lang.Object

org.drip.measure.continuous.R1Univariate

org.drip.measure.gaussian.R1UnivariateNormal

Direct Known Subclasses:

ConditionalPriceDistribution, PriorDriftDistribution, ShortfallIncrementDistribution

public class R1UnivariateNormal
extends R1Univariate

R1UnivariateNormal implements the Univariate R¹ Normal Distribution. It implements the Incremental, the Cumulative, and the Inverse Cumulative Distribution Densities.

• Module = Computational Core Module
• Library = Numerical Analysis Library
• Project = R^d Continuous/Discrete Probability Measures
• Package = R¹ R^d Covariant Gaussian Quadrature

Author:

Lakshmi Krishnamurthy

Constructor Summary

Constructors

Constructor	Description
R1UnivariateNormal(double dblMean, double dblSigma)	Construct a R1 Normal/Gaussian Distribution

Method Summary

Modifier and Type	Method	Description
double	confidence(double dblWidth)	Compute the Confidence given the Width around the Mean
double	confidenceInterval(double dblConfidence)	Compute the Width around the Mean given the Confidence Level
double	cumulative(double dblX)	Compute the cumulative under the distribution to the given value
double	density(double dblX)	Compute the Density under the Distribution at the given Variate
double	errorFunction(double dblX)	Compute the Error Function Around an Absolute Width around the Mean
Array2D	histogram()	Retrieve the Univariate Weighted Histogram
double	incremental(double dblXLeft, double dblXRight)	Compute the Incremental under the Distribution between the 2 variates
double	invCumulative(double dblY)	Compute the inverse cumulative under the distribution corresponding to the given value
double	mean()	Retrieve the Mean of the Distribution
double	median()	Retrieve the Median of the Distribution
double	mode()	Retrieve the Mode of the Distribution
double	random()	Generate a Random Variable corresponding to the Distribution
double	sigma()	Retrieve the Sigma
static R1UnivariateNormal	Standard()	Generate a N (0, 1) distribution
double[]	support()	Lay out the Support of the PDF Range
double	variance()	Retrieve the Variance of the Distribution

Methods inherited from class org.drip.measure.continuous.R1Univariate

bPOE, centralMoment, cvar, differentialEntropy, excessKurtosis, expectedShortfall, fisherInformation, iqr, kullbackLeiblerDivergence, momentGeneratingFunction, nonCentralMoment, populationCentralMeasures, probabilityGeneratingFunction, quantile, randomArray, skewness, supported, tukeyAnomaly, tukeyCriterion

Methods inherited from class java.lang.Object

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

Constructor Details

R1UnivariateNormal

public R1UnivariateNormal(double dblMean,
double dblSigma)
                   throws java.lang.Exception

Construct a R1 Normal/Gaussian Distribution

Parameters:

dblMean - Mean of the Distribution

dblSigma - Sigma of the Distribution

Throws:

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

Method Details

Standard

public static final R1UnivariateNormal Standard()

Generate a N (0, 1) distribution

Returns:

The N (0, 1) distribution

sigma

public double sigma()

Retrieve the Sigma

Returns:

The Sigma

support

public double[] support()

Description copied from class: R1Univariate

Lay out the Support of the PDF Range

Specified by:

support in class R1Univariate

Returns:

Support of the PDF Range

cumulative

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

Description copied from class: R1Univariate

Compute the cumulative under the distribution to the given value

Specified by:

cumulative in class R1Univariate

Parameters:

dblX - 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 dblXLeft,
double dblXRight)
                   throws java.lang.Exception

Description copied from class: R1Univariate

Compute the Incremental under the Distribution between the 2 variates

Overrides:

incremental in class R1Univariate

Parameters:

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

dblXRight - 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 dblY)
                     throws java.lang.Exception

Description copied from class: R1Univariate

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

Overrides:

invCumulative in class R1Univariate

Parameters:

dblY - 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 dblX)
               throws java.lang.Exception

Description copied from class: R1Univariate

Compute the Density under the Distribution at the given Variate

Specified by:

density in class R1Univariate

Parameters:

dblX - 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()

Description copied from class: R1Univariate

Retrieve the Mean of the Distribution

Specified by:

mean in class R1Univariate

Returns:

The Mean of the Distribution

median

public double median()

Description copied from class: R1Univariate

Retrieve the Median of the Distribution

Overrides:

median in class R1Univariate

Returns:

The Median of the Distribution

mode

public double mode()

Description copied from class: R1Univariate

Retrieve the Mode of the Distribution

Overrides:

mode in class R1Univariate

Returns:

The Mode of the Distribution

variance

public double variance()

Description copied from class: R1Univariate

Retrieve the Variance of the Distribution

Specified by:

variance in class R1Univariate

Returns:

The Variance of the Distribution

histogram

public Array2D histogram()

Description copied from class: R1Univariate

Retrieve the Univariate Weighted Histogram

Overrides:

histogram in class R1Univariate

Returns:

The Univariate Weighted Histogram

random

public double random()

Description copied from class: R1Univariate

Generate a Random Variable corresponding to the Distribution

Overrides:

random in class R1Univariate

Returns:

Random Variable corresponding to the Distribution

errorFunction

public double errorFunction(double dblX)
                     throws java.lang.Exception

Compute the Error Function Around an Absolute Width around the Mean

Parameters:

dblX - The Width

Returns:

The Error Function Around an Absolute Width around the Mean

Throws:

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

confidence

public double confidence(double dblWidth)
                  throws java.lang.Exception

Compute the Confidence given the Width around the Mean

Parameters:

dblWidth - The Width

Returns:

The Error Function Around an Absolute Width around the Mean

Throws:

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

confidenceInterval

public double confidenceInterval(double dblConfidence)
                          throws java.lang.Exception

Compute the Width around the Mean given the Confidence Level

Parameters:

dblConfidence - The Confidence Level

Returns:

The Width around the Mean given the Confidence Level

Throws:

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