R1Uniform.java
package org.drip.measure.lebesgue;
/*
* -*- 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
*
* 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>R1Uniform</i> implements the R<sup>1</sup> Lebesgue (i.e., Bounded Uniform) Distribution, with a
* Uniform Distribution between a Lower and an Upper Bound.
*
* <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/lebesgue/README.md">Uniform Piece-wise Lebesgue Measure</a></li>
* </ul>
*
* @author Lakshmi Krishnamurthy
*/
public class R1Uniform extends org.drip.measure.continuous.R1Univariate {
protected static final int GRID_WIDTH = 100;
private double _dblLeftPredictorOrdinateEdge = java.lang.Double.NaN;
private double _dblRightPredictorOrdinateEdge = java.lang.Double.NaN;
/**
* Construct a R^1 Bounded Uniform Distribution
*
* @param dblLeftPredictorOrdinateEdge The Left Predictor Ordinate Edge
* @param dblRightPredictorOrdinateEdge The Right Predictor Ordinate Edge
*
* @throws java.lang.Exception Thrown if the inputs are invalid
*/
public R1Uniform (
final double dblLeftPredictorOrdinateEdge,
final double dblRightPredictorOrdinateEdge)
throws java.lang.Exception
{
if (!org.drip.numerical.common.NumberUtil.IsValid (_dblLeftPredictorOrdinateEdge =
dblLeftPredictorOrdinateEdge) || !org.drip.numerical.common.NumberUtil.IsValid
(_dblRightPredictorOrdinateEdge = dblRightPredictorOrdinateEdge) ||
_dblRightPredictorOrdinateEdge <= _dblLeftPredictorOrdinateEdge)
throw new java.lang.Exception ("R1Uniform Constructor: Invalid Inputs");
}
/**
* Retrieve the Left Predictor Ordinate Edge
*
* @return The Left Predictor Ordinate Edge
*/
public double leftEdge()
{
return _dblLeftPredictorOrdinateEdge;
}
/**
* Retrieve the Right Predictor Ordinate Edge
*
* @return The Right Predictor Ordinat Edge
*/
public double rightEdge()
{
return _dblRightPredictorOrdinateEdge;
}
@Override public double[] support()
{
return new double[]
{
_dblLeftPredictorOrdinateEdge,
_dblRightPredictorOrdinateEdge
};
}
@Override public double cumulative (
final double dblX)
throws java.lang.Exception
{
if (!org.drip.numerical.common.NumberUtil.IsValid (dblX))
throw new java.lang.Exception ("R1Uniform::cumulative => Invalid Inputs");
if (dblX <= _dblLeftPredictorOrdinateEdge) return 0.;
if (dblX >= _dblRightPredictorOrdinateEdge) return 1.;
return (dblX - _dblLeftPredictorOrdinateEdge) / (_dblRightPredictorOrdinateEdge -
_dblLeftPredictorOrdinateEdge);
}
@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) || dblY < 0. || dblY > 1.)
throw new java.lang.Exception ("R1Uniform::invCumulative => Invalid inputs");
return dblY * (_dblRightPredictorOrdinateEdge - _dblLeftPredictorOrdinateEdge) +
_dblLeftPredictorOrdinateEdge;
}
@Override public double density (
final double dblX)
throws java.lang.Exception
{
return dblX <= _dblLeftPredictorOrdinateEdge || dblX >= _dblRightPredictorOrdinateEdge ? 0. : 1. /
(_dblRightPredictorOrdinateEdge - _dblLeftPredictorOrdinateEdge);
}
@Override public double mean()
{
return 0.5 * (_dblRightPredictorOrdinateEdge + _dblLeftPredictorOrdinateEdge);
}
@Override public double variance()
{
return (_dblRightPredictorOrdinateEdge - _dblLeftPredictorOrdinateEdge) *
(_dblRightPredictorOrdinateEdge - _dblLeftPredictorOrdinateEdge) / 12.;
}
@Override public org.drip.numerical.common.Array2D histogram()
{
double[] adblX = new double[GRID_WIDTH];
double[] adblY = new double[GRID_WIDTH];
double dblWidth = (_dblRightPredictorOrdinateEdge - _dblLeftPredictorOrdinateEdge) / GRID_WIDTH;
for (int i = 0; i < GRID_WIDTH; ++i) {
adblY[i] = 1. / GRID_WIDTH;
adblX[i] = _dblLeftPredictorOrdinateEdge + (i + 1) * dblWidth;
}
return org.drip.numerical.common.Array2D.FromArray (adblX, adblY);
}
}