BoundedSequenceAgnosticMetrics.java
package org.drip.sequence.metrics;
/*
* -*- mode: java; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*-
*/
/*!
* 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 risk, transaction costs, exposure, margin
* calculations, and portfolio construction within and across fixed income, credit, commodity, equity,
* FX, and structured products.
*
* https://lakshmidrip.github.io/DROP/
*
* DROP is composed of three main modules:
*
* - DROP Analytics Core - https://lakshmidrip.github.io/DROP-Analytics-Core/
* - DROP Portfolio Core - https://lakshmidrip.github.io/DROP-Portfolio-Core/
* - DROP Numerical Core - https://lakshmidrip.github.io/DROP-Numerical-Core/
*
* DROP Analytics Core implements libraries for the following:
* - Fixed Income Analytics
* - Asset Backed Analytics
* - XVA Analytics
* - Exposure and Margin Analytics
*
* DROP Portfolio Core implements libraries for the following:
* - Asset Allocation Analytics
* - Transaction Cost Analytics
*
* DROP Numerical Core implements libraries for the following:
* - Statistical Learning Library
* - Numerical Optimizer Library
* - Machine Learning Library
* - Spline Builder Library
*
* 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
* - 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>BoundedSequenceAgnosticMetrics</i> contains the Sample Distribution Metrics and Agnostic Bounds related
* to the specified Bounded Sequence.
*
* <br><br>
* <ul>
* <li><b>Module </b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/NumericalCore.md">Numerical Core Module</a></li>
* <li><b>Library</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/StatisticalLearningLibrary.md">Statistical Learning Library</a></li>
* <li><b>Project</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/src/main/java/org/drip/sequence">Sequence</a></li>
* <li><b>Package</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/src/main/java/org/drip/sequence/metrics">Metrics</a></li>
* </ul>
* <br><br>
*
* @author Lakshmi Krishnamurthy
*/
public class BoundedSequenceAgnosticMetrics extends
org.drip.sequence.metrics.SingleSequenceAgnosticMetrics {
private double _dblSupport = java.lang.Double.NaN;
/**
* BoundedSequenceAgnosticMetrics Constructor
*
* @param adblSequence The Random Sequence
* @param distPopulation The Population Distribution
* @param dblSupport The Support of the Underlying Random Variable
*
* @throws java.lang.Exception Thrown if BoundedSequenceAgnosticMetrics cannot be constructed
*/
public BoundedSequenceAgnosticMetrics (
final double[] adblSequence,
final org.drip.measure.continuous.R1Univariate distPopulation,
final double dblSupport)
throws java.lang.Exception
{
super (adblSequence, distPopulation);
if (!org.drip.numerical.common.NumberUtil.IsValid (_dblSupport = dblSupport) || 0. >= _dblSupport)
throw new java.lang.Exception ("BoundedSequenceAgnosticMetrics ctr: Invalid Inputs");
}
/**
* Retrieve the Random Sequence Support
*
* @return The Support Underlying the Random Sequence
*/
public double support()
{
return _dblSupport;
}
/**
* Estimate Mean Departure Bounds of the Average using the Chernoff-Hoeffding Bound
*
* @param dblLevel The Level at which the Departure is sought
*
* @return The Mean Departure Bounds
*/
public org.drip.sequence.metrics.PivotedDepartureBounds chernoffHoeffdingAverageBounds (
final double dblLevel)
{
if (!org.drip.numerical.common.NumberUtil.IsValid (dblLevel) || dblLevel <= 0) return null;
double dblBound = java.lang.Math.exp (-2. * sequence().length * dblLevel * dblLevel / (_dblSupport *
_dblSupport));
dblBound = dblBound < 1. ? dblBound : 1.;
try {
return new org.drip.sequence.metrics.PivotedDepartureBounds
(org.drip.sequence.metrics.PivotedDepartureBounds.PIVOT_ANCHOR_TYPE_MEAN,
java.lang.Double.NaN, dblBound, dblBound);
} catch (java.lang.Exception e) {
e.printStackTrace();
}
return null;
}
/**
* Estimate Mean Departure Bounds of the Average using the Bennett Inequality Bounds
*
* @param dblLevel The Level at which the Departure is sought
*
* @return The Mean Departure Bounds
*/
public org.drip.sequence.metrics.PivotedDepartureBounds bennettAverageBounds (
final double dblLevel)
{
if (!org.drip.numerical.common.NumberUtil.IsValid (dblLevel) || dblLevel <= 0.) return null;
try {
double dblPopulationVariance = populationVariance();
double dblVariance = (org.drip.numerical.common.NumberUtil.IsValid (dblPopulationVariance) ?
dblPopulationVariance : empiricalVariance());
double dblBennettFactor = _dblSupport * dblLevel / dblVariance;
dblBennettFactor = (1. + dblBennettFactor) * java.lang.Math.log (1. + dblBennettFactor) -
dblBennettFactor;
double dblBound = java.lang.Math.exp (-1. * sequence().length * dblVariance * dblBennettFactor /
(_dblSupport * _dblSupport));
dblBound = dblBound < 1. ? dblBound : 1.;
return new org.drip.sequence.metrics.PivotedDepartureBounds
(org.drip.sequence.metrics.PivotedDepartureBounds.PIVOT_ANCHOR_TYPE_MEAN,
java.lang.Double.NaN, dblBound, dblBound);
} catch (java.lang.Exception e) {
e.printStackTrace();
}
return null;
}
/**
* Estimate Mean Departure Bounds of the Average using the Bernstein Inequality Bounds
*
* @param dblLevel The Level at which the Departure is sought
*
* @return The Mean Departure Bounds
*/
public org.drip.sequence.metrics.PivotedDepartureBounds bernsteinAverageBounds (
final double dblLevel)
{
if (!org.drip.numerical.common.NumberUtil.IsValid (dblLevel) || dblLevel <= 0.) return null;
try {
double dblPopulationVariance = populationVariance();
double dblVariance = (org.drip.numerical.common.NumberUtil.IsValid (dblPopulationVariance) ?
dblPopulationVariance : empiricalVariance());
double dblBound = java.lang.Math.exp (-1. * sequence().length * dblLevel * dblLevel / (2. *
dblVariance + (2. * _dblSupport * dblLevel / 3.)));
dblBound = dblBound < 1. ? dblBound : 1.;
return new org.drip.sequence.metrics.PivotedDepartureBounds
(org.drip.sequence.metrics.PivotedDepartureBounds.PIVOT_ANCHOR_TYPE_MEAN,
java.lang.Double.NaN, dblBound, dblBound);
} catch (java.lang.Exception e) {
e.printStackTrace();
}
return null;
}
}