PoissonSequenceAgnosticMetrics.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>PoissonSequenceAgnosticMetrics</i> contains the Sample Distribution Metrics and Agnostic Bounds related
 * to the specified Poisson 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 PoissonSequenceAgnosticMetrics extends org.drip.sequence.metrics.SingleSequenceAgnosticMetrics {
    private double _dblPopulationMean = java.lang.Double.NaN;

    /**
     * PoissonSequenceAgnosticMetrics Constructor
     * 
     * @param adblSequence The Random Sequence
     * @param dblPopulationMean The Mean of the Underlying Distribution
     * 
     * @throws java.lang.Exception Thrown if PoissonSequenceAgnosticMetrics cannot be constructed
     */

    public PoissonSequenceAgnosticMetrics (
        final double[] adblSequence,
        final double dblPopulationMean)
        throws java.lang.Exception
    {
        super (adblSequence, null);

        _dblPopulationMean = dblPopulationMean;
    }

    /**
     * Retrieve the Mean of the Underlying Distribution
     * 
     * @return The Mean of the Underlying Distribution
     */

    public double populationMean()
    {
        return _dblPopulationMean;
    }

    /**
     * Compute the Chernoff-Stirling Upper Bound
     * 
     * @param dblLevel The Level at which the Bound is sought
     * 
     * @return The Chernoff-Stirling Upper Bound
     * 
     * @throws java.lang.Exception Thrown if the Chernoff-Stirling Upper Bound cannot be computed
     */

    public double chernoffStirlingUpperBound (
        final double dblLevel)
        throws java.lang.Exception
    {
        if (!org.drip.numerical.common.NumberUtil.IsValid (dblLevel))
            throw new java.lang.Exception
                ("PoissonSequenceAgnosticMetrics::chernoffStirlingUpperBound => Invalid Inputs");

        int iNumEntry = sequence().length;

        double dblPopulationMean = org.drip.numerical.common.NumberUtil.IsValid (_dblPopulationMean) ?
            _dblPopulationMean : empiricalExpectation();

        double dblBound = (java.lang.Math.pow (dblPopulationMean / dblLevel, iNumEntry * dblLevel) *
            java.lang.Math.exp (iNumEntry * (dblLevel - dblPopulationMean) - (1. / (12. * iNumEntry *
                dblLevel + 1.)))) / java.lang.Math.sqrt (2. * java.lang.Math.PI * iNumEntry * dblLevel);

        if (!org.drip.numerical.common.NumberUtil.IsValid (dblBound)) return 0.;

        return dblBound > 1. ? 1. : dblBound;
    }
}