R1UnivariateNormal.java
package org.drip.measure.gaussian;
/*
* -*- mode: java; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*-
*/
/*!
* Copyright (C) 2020 Lakshmi Krishnamurthy
* Copyright (C) 2019 Lakshmi Krishnamurthy
* Copyright (C) 2018 Lakshmi Krishnamurthy
* Copyright (C) 2017 Lakshmi Krishnamurthy
* Copyright (C) 2016 Lakshmi Krishnamurthy
* Copyright (C) 2015 Lakshmi Krishnamurthy
* Copyright (C) 2014 Lakshmi Krishnamurthy
* Copyright (C) 2013 Lakshmi Krishnamurthy
*
* This file is part of DROP, an open-source library targeting analytics/risk, transaction cost analytics,
* asset liability management analytics, capital, exposure, and margin analytics, valuation adjustment
* analytics, and portfolio construction analytics within and across fixed income, credit, commodity,
* equity, FX, and structured products. It also includes auxiliary libraries for algorithm support,
* numerical analysis, numerical optimization, spline builder, model validation, statistical learning,
* and computational support.
*
* https://lakshmidrip.github.io/DROP/
*
* DROP is composed of three modules:
*
* - DROP Product Core - https://lakshmidrip.github.io/DROP-Product-Core/
* - DROP Portfolio Core - https://lakshmidrip.github.io/DROP-Portfolio-Core/
* - DROP Computational Core - https://lakshmidrip.github.io/DROP-Computational-Core/
*
* DROP Product Core implements libraries for the following:
* - Fixed Income Analytics
* - Loan Analytics
* - Transaction Cost Analytics
*
* DROP Portfolio Core implements libraries for the following:
* - Asset Allocation Analytics
* - Asset Liability Management Analytics
* - Capital Estimation Analytics
* - Exposure Analytics
* - Margin Analytics
* - XVA Analytics
*
* DROP Computational Core implements libraries for the following:
* - Algorithm Support
* - Computation Support
* - Function Analysis
* - Model Validation
* - Numerical Analysis
* - Numerical Optimizer
* - Spline Builder
* - Statistical Learning
*
* Documentation for DROP is Spread Over:
*
* - Main => https://lakshmidrip.github.io/DROP/
* - Wiki => https://github.com/lakshmiDRIP/DROP/wiki
* - GitHub => https://github.com/lakshmiDRIP/DROP
* - Repo Layout Taxonomy => https://github.com/lakshmiDRIP/DROP/blob/master/Taxonomy.md
* - Javadoc => https://lakshmidrip.github.io/DROP/Javadoc/index.html
* - Technical Specifications => https://github.com/lakshmiDRIP/DROP/tree/master/Docs/Internal
* - Release Versions => https://lakshmidrip.github.io/DROP/version.html
* - Community Credits => https://lakshmidrip.github.io/DROP/credits.html
* - Issues Catalog => https://github.com/lakshmiDRIP/DROP/issues
* - JUnit => https://lakshmidrip.github.io/DROP/junit/index.html
* - Jacoco => https://lakshmidrip.github.io/DROP/jacoco/index.html
*
* Licensed under the Apache License, Version 2.0 (the "License");
* you may not use this file except in compliance with the License.
*
* You may obtain a copy of the License at
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
*
* See the License for the specific language governing permissions and
* limitations under the License.
*/
/**
* <i>R1UnivariateNormal</i> implements the Univariate R<sup>1</sup> Normal Distribution. It implements the
* Incremental, the Cumulative, and the Inverse Cumulative Distribution Densities.
*
* <br><br>
* <ul>
* <li><b>Module </b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/ComputationalCore.md">Computational Core Module</a></li>
* <li><b>Library</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/NumericalAnalysisLibrary.md">Numerical Analysis Library</a></li>
* <li><b>Project</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/src/main/java/org/drip/measure/README.md">R<sup>d</sup> Continuous/Discrete Probability Measures</a></li>
* <li><b>Package</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/src/main/java/org/drip/measure/gaussian/README.md">R<sup>1</sup> R<sup>d</sup> Covariant Gaussian Quadrature</a></li>
* </ul>
*
* @author Lakshmi Krishnamurthy
*/
public class R1UnivariateNormal extends org.drip.measure.continuous.R1Univariate {
private double _dblMean = java.lang.Double.NaN;
private double _dblSigma = java.lang.Double.NaN;
/**
* Generate a N (0, 1) distribution
*
* @return The N (0, 1) distribution
*/
public static final org.drip.measure.gaussian.R1UnivariateNormal Standard()
{
try {
return new R1UnivariateNormal (0., 1.);
} catch (java.lang.Exception e) {
e.printStackTrace();
}
return null;
}
/**
* Construct a R1 Normal/Gaussian Distribution
*
* @param dblMean Mean of the Distribution
* @param dblSigma Sigma of the Distribution
*
* @throws java.lang.Exception Thrown if the inputs are invalid
*/
public R1UnivariateNormal (
final double dblMean,
final double dblSigma)
throws java.lang.Exception
{
if (!org.drip.numerical.common.NumberUtil.IsValid (_dblMean = dblMean) ||
!org.drip.numerical.common.NumberUtil.IsValid (_dblSigma = dblSigma) || 0. > _dblSigma)
throw new java.lang.Exception ("R1UnivariateNormal Constructor: Invalid Inputs");
}
/**
* Retrieve the Sigma
*
* @return The Sigma
*/
public double sigma()
{
return _dblSigma;
}
@Override public double[] support()
{
return new double[]
{
java.lang.Double.NEGATIVE_INFINITY,
java.lang.Double.POSITIVE_INFINITY
};
}
@Override public double cumulative (
final double dblX)
throws java.lang.Exception
{
if (!org.drip.numerical.common.NumberUtil.IsValid (dblX))
throw new java.lang.Exception ("R1UnivariateNormal::cumulative => Invalid Inputs");
if (0. == _dblSigma) return dblX >= _dblMean ? 1. : 0.;
return org.drip.measure.gaussian.NormalQuadrature.CDF ((dblX - _dblMean) / _dblSigma);
}
@Override public double incremental (
final double dblXLeft,
final double dblXRight)
throws java.lang.Exception
{
return cumulative (dblXRight) - cumulative (dblXLeft);
}
@Override public double invCumulative (
final double dblY)
throws java.lang.Exception
{
if (!org.drip.numerical.common.NumberUtil.IsValid (dblY) || 0. == _dblSigma)
throw new java.lang.Exception ("R1UnivariateNormal::invCumulative => Cannot calculate");
return org.drip.measure.gaussian.NormalQuadrature.InverseCDF (dblY) * _dblSigma + _dblMean;
}
@Override public double density (
final double dblX)
throws java.lang.Exception
{
if (!org.drip.numerical.common.NumberUtil.IsValid (dblX))
throw new java.lang.Exception ("R1UnivariateNormal::density => Invalid Inputs");
if (0. == _dblSigma) return dblX == _dblMean ? 1. : 0.;
double dblMeanShift = (dblX - _dblMean) / _dblSigma;
return java.lang.Math.exp (-0.5 * dblMeanShift * dblMeanShift);
}
@Override public double mean()
{
return _dblMean;
}
@Override public double median()
{
return _dblMean;
}
@Override public double mode()
{
return _dblMean;
}
@Override public double variance()
{
return _dblSigma * _dblSigma;
}
@Override public org.drip.numerical.common.Array2D histogram()
{
return null;
}
@Override public double random()
{
try
{
return invCumulative (java.lang.Math.random());
}
catch (java.lang.Exception e)
{
e.printStackTrace();
}
return java.lang.Double.NaN;
}
/**
* Compute the Error Function Around an Absolute Width around the Mean
*
* @param dblX The Width
*
* @return The Error Function Around an Absolute Width around the Mean
*
* @throws java.lang.Exception Thrown if the Inputs are Invalid
*/
public double errorFunction (
final double dblX)
throws java.lang.Exception
{
if (!org.drip.numerical.common.NumberUtil.IsValid (dblX))
throw new java.lang.Exception ("R1UnivariateNormal::errorFunction => Invalid Inputs");
double dblWidth = java.lang.Math.abs (dblX);
return cumulative (_dblMean + dblWidth) - cumulative (_dblMean - dblWidth);
}
/**
* Compute the Confidence given the Width around the Mean
*
* @param dblWidth The Width
*
* @return The Error Function Around an Absolute Width around the Mean
*
* @throws java.lang.Exception Thrown if the Inputs are Invalid
*/
public double confidence (
final double dblWidth)
throws java.lang.Exception
{
return errorFunction (dblWidth);
}
/**
* Compute the Width around the Mean given the Confidence Level
*
* @param dblConfidence The Confidence Level
*
* @return The Width around the Mean given the Confidence Level
*
* @throws java.lang.Exception Thrown if the Inputs are Invalid
*/
public double confidenceInterval (
final double dblConfidence)
throws java.lang.Exception
{
if (!org.drip.numerical.common.NumberUtil.IsValid (dblConfidence) || 0. >= dblConfidence || 1. <=
dblConfidence)
throw new java.lang.Exception ("R1UnivariateNormal::confidenceInterval => Invalid Inputs");
return invCumulative (0.5 * (1. + dblConfidence));
}
}