R1UnivariateExponential.java

package org.drip.measure.continuous;

/*
 * -*- mode: java; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*-
 */

/*!
 * Copyright (C) 2020 Lakshmi Krishnamurthy
 * Copyright (C) 2019 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>R1UnivariateExponential</i> implements the Univariate R<sup>1</sup> Exponential 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/continuous/README.md">R<sup>1</sup> and R<sup>d</sup> Continuous Random Measure</a></li>
 *  </ul>
 *
 * @author Lakshmi Krishnamurthy
 */

public class R1UnivariateExponential extends org.drip.measure.continuous.R1Univariate
{
    private double _lambda = java.lang.Double.NaN;

    /**
     * Construct the Standard R1UnivariateExponential Distribution (lambda = 1.)
     * 
     * @return The Standard R1UnivariateExponential Distribution
     */

    public static final R1UnivariateExponential Standard()
    {
        try
        {
            return new R1UnivariateExponential (1.);
        }
        catch (java.lang.Exception e)
        {
            e.printStackTrace();
        }

        return null;
    }

    /**
     * R1UnivariateExponential Constructor
     * 
     * @param lambda Lambda (Inverse Scaling Parameter)
     * 
     * @throws java.lang.Exception Thrown if the Inputs are Invalid
     */

    public R1UnivariateExponential (
        final double lambda)
        throws java.lang.Exception
    {
        if (!org.drip.numerical.common.NumberUtil.IsValid (_lambda = lambda) || 0. >= _lambda)
        {
            throw new java.lang.Exception ("R1UnivariateExponential Constructor => Invalid Inputs: " + _lambda);
        }
    }

    /**
     * Retrieve the Lambda (Inverse Scaling Parameter)
     * 
     * @return The Lambda (Inverse Scaling Parameter)
     */

    public double lambda()
    {
        return _lambda;
    }

    @Override public double[] support()
    {
        return new double[]
        {
            0.,
            java.lang.Double.POSITIVE_INFINITY
        };
    }

    @Override public double cumulative (
        final double x)
        throws java.lang.Exception
    {
        if (!org.drip.numerical.common.NumberUtil.IsValid (x) || x < 0.)
            throw new java.lang.Exception ("R1UnivariateExponential::cumulative => Invalid Inputs");

        return 1. - java.lang.Math.exp (-1. * _lambda * x);
    }

    @Override public double incremental (
        final double xLeft,
        final double xRight)
        throws java.lang.Exception
    {
        return cumulative (xLeft) - cumulative (xRight);
    }

    @Override public double invCumulative (
        final double y)
        throws java.lang.Exception
    {
        if (!org.drip.numerical.common.NumberUtil.IsValid (y) || 1. < y || 0. > y)
            throw new java.lang.Exception ("R1UnivariateExponential::invCumulative => Cannot calculate");

        return -1. / _lambda * java.lang.Math.log (1. - y);
    }

    @Override public double density (
        final double x)
        throws java.lang.Exception
    {
        if (!org.drip.numerical.common.NumberUtil.IsValid (x) || x < 0.)
            throw new java.lang.Exception ("R1UnivariateExponential::density => Invalid Inputs");

        return _lambda * java.lang.Math.exp (-1. * _lambda * x);
    }

    @Override public double mean()
    {
        return 1. / _lambda;
    }

    @Override public double variance()
    {
        return 1. / (_lambda * _lambda);
    }

    @Override public org.drip.numerical.common.Array2D histogram()
    {
        return null;
    }
}