R1Univariate.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
* 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>R1Univariate</i> exposes the Base Abstract Class behind Univariate R<sup>1</sup> Distributions. It
* exports the Methods for incremental, cumulative, and 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 abstract class R1Univariate {
/**
* Lay out the Support of the PDF Range
*
* @return Support of the PDF Range
*/
public abstract double[] support();
/**
* Indicate if x is inside the Supported Range
*
* @param x X
*
* @return TRUE - x is inside of the Supported Range
*/
public boolean supported (
final double x)
{
if (java.lang.Double.isNaN (x))
{
return false;
}
double[] range = support();
return range[0] <= x && x <= range[1];
}
/**
* Compute the Density under the Distribution at the given Variate
*
* @param dblX Variate at which the Density needs to be computed
*
* @return The Density
*
* @throws java.lang.Exception Thrown if the input is invalid
*/
public abstract double density (
final double dblX)
throws java.lang.Exception;
/**
* Compute the cumulative under the distribution to the given value
*
* @param dblX Variate to which the cumulative is to be computed
*
* @return The cumulative
*
* @throws java.lang.Exception Thrown if the inputs are invalid
*/
public abstract double cumulative (
final double dblX)
throws java.lang.Exception;
/**
* Compute the Incremental under the Distribution between the 2 variates
*
* @param dblXLeft Left Variate to which the cumulative is to be computed
* @param dblXRight Right Variate to which the cumulative is to be computed
*
* @return The Incremental under the Distribution between the 2 variates
*
* @throws java.lang.Exception Thrown if the inputs are invalid
*/
public double incremental (
final double dblXLeft,
final double dblXRight)
throws java.lang.Exception
{
return cumulative (dblXRight) - cumulative (dblXLeft);
}
/**
* Compute the inverse cumulative under the distribution corresponding to the given value
*
* @param p Value corresponding to which the inverse cumulative is to be computed
*
* @return The inverse cumulative
*
* @throws java.lang.Exception Thrown if the Input is invalid
*/
public double invCumulative (
final double p)
throws java.lang.Exception
{
if (!org.drip.numerical.common.NumberUtil.IsValid (p) || 0. > p || 1. < p)
{
throw new java.lang.Exception ("R1Univariate::invCumulative => Invalid Inputs");
}
org.drip.function.r1tor1solver.FixedPointFinderOutput fixedPointFinderOutput =
new org.drip.function.r1tor1solver.FixedPointFinderBrent (
0.,
new org.drip.function.definition.R1ToR1 (null)
{
@Override public double evaluate (
final double u)
throws java.lang.Exception
{
return cumulative (u) - p;
}
},
true
).findRoot();
if (null == fixedPointFinderOutput)
{
throw new java.lang.Exception ("R1Univariate::invCumulative => Cannot find Root");
}
return fixedPointFinderOutput.getRoot();
}
/**
* Retrieve the Mean of the Distribution
*
* @return The Mean of the Distribution
*
* @throws java.lang.Exception Thrown if the Mean cannot be estimated
*/
public abstract double mean()
throws java.lang.Exception;
/**
* Retrieve the Median of the Distribution
*
* @return The Median of the Distribution
*
* @throws java.lang.Exception Thrown if the Median cannot be estimated
*/
public double median()
throws java.lang.Exception
{
return invCumulative (0.50);
}
/**
* Retrieve the Mode of the Distribution
*
* @return The Mode of the Distribution
*
* @throws java.lang.Exception Thrown if the Mode cannot be estimated
*/
public double mode()
throws java.lang.Exception
{
final org.drip.function.definition.R1ToR1 densityFunction =
new org.drip.function.definition.R1ToR1 (null)
{
@Override public double evaluate (
final double u)
throws java.lang.Exception
{
return density (u);
}
};
org.drip.function.r1tor1solver.FixedPointFinderOutput fixedPointFinderOutput =
new org.drip.function.r1tor1solver.FixedPointFinderBrent (
0.,
new org.drip.function.definition.R1ToR1 (null)
{
@Override public double evaluate (
final double u)
throws java.lang.Exception
{
return densityFunction.derivative (
u,
1
);
}
},
true
).findRoot();
if (null == fixedPointFinderOutput)
{
throw new java.lang.Exception ("R1Univariate::invCumulative => Cannot find Root");
}
return fixedPointFinderOutput.getRoot();
}
/**
* Retrieve the Variance of the Distribution
*
* @return The Variance of the Distribution
*
* @throws java.lang.Exception Thrown if the Variance cannot be estimated
*/
public abstract double variance()
throws java.lang.Exception;
/**
* Retrieve the Skewness of the Distribution
*
* @return The Skewness of the Distribution
*
* @throws java.lang.Exception Thrown if the Skewness cannot be estimated
*/
public double skewness()
throws java.lang.Exception
{
throw new java.lang.Exception ("R1Univariate::skewness => Not implemented");
}
/**
* Retrieve the Excess Kurtosis of the Distribution
*
* @return The Excess Kurtosis of the Distribution
*
* @throws java.lang.Exception Thrown if the Skewness cannot be estimated
*/
public double excessKurtosis()
throws java.lang.Exception
{
throw new java.lang.Exception ("R1Univariate::excessKurtosis => Not implemented");
}
/**
* Retrieve the Differential Entropy of the Distribution
*
* @return The Differential Entropy of the Distribution
*
* @throws java.lang.Exception Thrown if the Entropy cannot be estimated
*/
public double differentialEntropy()
throws java.lang.Exception
{
return org.drip.numerical.integration.NewtonCotesQuadratureGenerator.GaussLaguerreLeftDefinite (
0.,
10000
).integrate (
new org.drip.function.definition.R1ToR1 (null)
{
@Override public double evaluate (
final double t)
throws java.lang.Exception
{
double density = density (t);
return density * java.lang.Math.log (density);
}
}
);
}
/**
* Construct the Moment Generating Function
*
* @return The Moment Generating Function
*/
public org.drip.function.definition.R1ToR1 momentGeneratingFunction()
{
return null;
}
/**
* Construct the Probability Generating Function
*
* @return The Probability Generating Function
*/
public org.drip.function.definition.R1ToR1 probabilityGeneratingFunction()
{
return null;
}
/**
* Generate a Random Variable corresponding to the Distribution
*
* @return Random Variable corresponding to the Distribution
*
* @throws java.lang.Exception Thrown if the Random Instance cannot be estimated
*/
public double random()
throws java.lang.Exception
{
return invCumulative (java.lang.Math.random());
}
/**
* Retrieve the Array of Generated Random Variables
*
* @param arrayCount Number of Elements
*
* @return Array of Generated Random Variables
*/
public double[] randomArray (
final int arrayCount)
{
if (0 >= arrayCount)
{
return null;
}
double[] randomArray = new double[arrayCount];
for (int index = 0; index < arrayCount; ++index)
{
try
{
randomArray[index] = random();
}
catch (java.lang.Exception e)
{
e.printStackTrace();
return null;
}
}
return randomArray;
}
/**
* Retrieve the Population Central Measures
*
* @return The Population Central Measures
*/
public org.drip.measure.statistics.PopulationCentralMeasures populationCentralMeasures()
{
try
{
return new org.drip.measure.statistics.PopulationCentralMeasures (
mean(),
variance()
);
}
catch (java.lang.Exception e)
{
e.printStackTrace();
}
return null;
}
/**
* Retrieve the Univariate Weighted Histogram
*
* @return The Univariate Weighted Histogram
*/
public org.drip.numerical.common.Array2D histogram()
{
return null;
}
}