java.lang.Object

org.drip.measure.distribution.R1Continuous

org.drip.measure.gaussian.R1UnivariateNormal

Direct Known Subclasses:: ConditionalPriceDistribution, PriorDriftDistribution, ShortfallIncrementDistribution

public class R1UnivariateNormal
extends R1Continuous

R1UnivariateNormal implements the Univariate R¹ Normal Distribution. It implements the Incremental, the Cumulative, and the Inverse Cumulative Distribution Densities. It provides the following Functionality:

Generate a N (0, 1) distribution
Construct a R1 Normal/Gaussian Distribution
Retrieve the Sigma
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 Median of the Distribution
Retrieve the Mode of the Distribution
Retrieve the Variance of the Distribution
Retrieve the Univariate Weighted Histogram
Generate a Random Variable corresponding to the Distribution
Compute the Error Function Around an Absolute Width around the Mean
Compute the Confidence given the Width around the Mean
Compute the Width around the Mean given the Confidence Level

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

Author:: Lakshmi Krishnamurthy

Constructor Summary

Constructors

Constructor Description

R1UnivariateNormal(double mean, double sigma)
Construct a R1 Normal/Gaussian Distribution

Method Summary

Modifier and Type	Method	Description
`double`	`confidence(double width)`	Compute the Confidence given the Width around the Mean
`double`	`confidenceInterval(double confidence)`	Compute the Width around the Mean given the Confidence Level
`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
`double`	`errorFunction(double x)`	Compute the Error Function Around an Absolute Width around the Mean
`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 y)`	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.distribution.R1Continuous

bPOE, centralMoment, cvar, differentialEntropy, excessKurtosis, expectedShortfall, fisherInformation, iqr, kullbackLeiblerDivergence, nonCentralMoment, populationCentralMeasures, probabilityGeneratingFunction, quadratureEstimator, 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 mean, double sigma) throws java.lang.Exception
  
  Construct a R1 Normal/Gaussian Distribution
  
  Parameters:
  
  mean - Mean of the Distribution
  
  sigma - 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()
  
  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 y) throws java.lang.Exception
  
  Compute the inverse cumulative under the distribution corresponding to the given value
  
  Overrides:
  
  invCumulative in class R1Continuous
  
  Parameters:
  
  y - 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
- median
  
  public double median()
  
  Retrieve the Median of the Distribution
  
  Overrides:
  
  median in class R1Continuous
  
  Returns:
  
  The Median of the Distribution
  
  Throws:
  
  java.lang.Exception - Thrown if the Median cannot be estimated
- mode
  
  public double mode()
  
  Retrieve the Mode of the Distribution
  
  Overrides:
  
  mode in class R1Continuous
  
  Returns:
  
  The Mode of the Distribution
  
  Throws:
  
  java.lang.Exception - Thrown if the Mode 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
- histogram
  
  public Array2D histogram()
  
  Retrieve the Univariate Weighted Histogram
  
  Overrides:
  
  histogram in class R1Continuous
  
  Returns:
  
  The Univariate Weighted Histogram
- 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
- errorFunction
  
  public double errorFunction(double x) throws java.lang.Exception
  
  Compute the Error Function Around an Absolute Width around the Mean
  
  Parameters:
  
  x - 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 width) throws java.lang.Exception
  
  Compute the Confidence given the Width around the Mean
  
  Parameters:
  
  width - 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 confidence) throws java.lang.Exception
  
  Compute the Width around the Mean given the Confidence Level
  
  Parameters:
  
  confidence - The Confidence Level
  
  Returns:
  
  The Width around the Mean given the Confidence Level
  
  Throws:
  
  java.lang.Exception - Thrown if the Inputs are Invalid

Class R1UnivariateNormal

Constructor Summary

Method Summary

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

Methods inherited from class java.lang.Object

Constructor Details

R1UnivariateNormal

Method Details

Standard

sigma

support

cumulative

incremental

invCumulative

density

mean

median

mode

variance

histogram

random

errorFunction

confidence

confidenceInterval