IIDSequenceSumBound.java

package org.drip.sample.sequence;

import org.drip.measure.continuous.R1Univariate;
import org.drip.measure.lebesgue.R1Uniform;
import org.drip.numerical.common.FormatUtil;
import org.drip.sequence.metrics.*;
import org.drip.sequence.random.*;
import org.drip.service.env.EnvManager;

/*

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

/*!
 * 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 DRIP, a free-software/open-source library for buy/side financial/trading model
 *      libraries targeting analysts and developers
 *      https://lakshmidrip.github.io/DRIP/
 *  
 *  DRIP is composed of four main libraries:
 *  
 *  - DRIP Fixed Income - https://lakshmidrip.github.io/DRIP-Fixed-Income/
 *  - DRIP Asset Allocation - https://lakshmidrip.github.io/DRIP-Asset-Allocation/
 *  - DRIP Numerical Optimizer - https://lakshmidrip.github.io/DRIP-Numerical-Optimizer/
 *  - DRIP Statistical Learning - https://lakshmidrip.github.io/DRIP-Statistical-Learning/
 * 
 *  - DRIP Fixed Income: Library for Instrument/Trading Conventions, Treasury Futures/Options,
 *      Funding/Forward/Overnight Curves, Multi-Curve Construction/Valuation, Collateral Valuation and XVA
 *      Metric Generation, Calibration and Hedge Attributions, Statistical Curve Construction, Bond RV
 *      Metrics, Stochastic Evolution and Option Pricing, Interest Rate Dynamics and Option Pricing, LMM
 *      Extensions/Calibrations/Greeks, Algorithmic Differentiation, and Asset Backed Models and Analytics.
 * 
 *  - DRIP Asset Allocation: Library for model libraries for MPT framework, Black Litterman Strategy
 *      Incorporator, Holdings Constraint, and Transaction Costs.
 * 
 *  - DRIP Numerical Optimizer: Library for Numerical Optimization and Spline Functionality.
 * 
 *  - DRIP Statistical Learning: Library for Statistical Evaluation and Machine Learning.
 * 
 *  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.
 */

/**
 * IIDSequenceSumBound demonstrates the Computation of the Different Probabilistic Bounds for Sums of i.i.d.
 *  Random Sequences.
 *
 * @author Lakshmi Krishnamurthy
 */

public class IIDSequenceSumBound {

    private static final void Head (
        final String strHeader)
    {
        System.out.println();

        System.out.println ("\t|---------------------------------------------------------------------------------------|");

        System.out.println (strHeader);

        System.out.println ("\t|---------------------------------------------------------------------------------------|");

        System.out.println ("\t|   SAMPLE  ||               <-               TOLERANCES               ->               |");

        System.out.println ("\t|---------------------------------------------------------------------------------------|");
    }

    private static final void WeakLawBounds (
        final UnivariateSequenceGenerator iidsg,
        final R1Univariate dist,
        final int[] aiSampleSize,
        final double[] adblTolerance)
        throws Exception
    {
        for (int iSampleSize : aiSampleSize) {
            SingleSequenceAgnosticMetrics ssamDist = iidsg.sequence (
                iSampleSize,
                dist
            );

            String strDump = "\t| " + FormatUtil.FormatDouble (iSampleSize, 8, 0, 1) + " => ";

            for (double dblTolerance : adblTolerance)
                strDump += FormatUtil.FormatDouble (ssamDist.weakLawAverageBounds (dblTolerance).upper(), 1, 9, 1.) + " | ";

            System.out.println (strDump);
        }
    }

    private static final void ChernoffHoeffdingBounds (
        final UnivariateSequenceGenerator iidsg,
        final R1Univariate dist,
        final double dblSupport,
        final int[] aiSampleSize,
        final double[] adblTolerance)
        throws Exception
    {
        for (int iSampleSize : aiSampleSize) {
            BoundedSequenceAgnosticMetrics ssamDist = (BoundedSequenceAgnosticMetrics) iidsg.sequence (
                iSampleSize,
                dist
            );

            String strDump = "\t| " + FormatUtil.FormatDouble (iSampleSize, 8, 0, 1) + " => ";

            for (double dblTolerance : adblTolerance)
                strDump += FormatUtil.FormatDouble (ssamDist.chernoffHoeffdingAverageBounds (dblTolerance).upper(), 1, 9, 1.) + " | ";

            System.out.println (strDump);
        }
    }

    private static final void BennettBounds (
        final UnivariateSequenceGenerator iidsg,
        final R1Univariate dist,
        final double dblSupport,
        final int[] aiSampleSize,
        final double[] adblTolerance)
        throws Exception
    {
        for (int iSampleSize : aiSampleSize) {
            BoundedSequenceAgnosticMetrics ssamDist = (BoundedSequenceAgnosticMetrics) iidsg.sequence (
                iSampleSize,
                dist
            );

            String strDump = "\t| " + FormatUtil.FormatDouble (iSampleSize, 8, 0, 1) + " => ";

            for (double dblTolerance : adblTolerance)
                strDump += FormatUtil.FormatDouble (ssamDist.bennettAverageBounds (dblTolerance).upper(), 1, 9, 1.) + " | ";

            System.out.println (strDump);
        }
    }

    private static final void BernsteinBounds (
        final UnivariateSequenceGenerator iidsg,
        final R1Univariate dist,
        final double dblSupport,
        final int[] aiSampleSize,
        final double[] adblTolerance)
        throws Exception
    {
        for (int iSampleSize : aiSampleSize) {
            BoundedSequenceAgnosticMetrics ssamDist = (BoundedSequenceAgnosticMetrics) iidsg.sequence (
                iSampleSize,
                dist
            );

            String strDump = "\t| " + FormatUtil.FormatDouble (iSampleSize, 8, 0, 1) + " => ";

            for (double dblTolerance : adblTolerance)
                strDump += FormatUtil.FormatDouble (ssamDist.bernsteinAverageBounds (dblTolerance).upper(), 1, 9, 1.) + " | ";

            System.out.println (strDump);
        }
    }

    public static void main (
        final String[] args)
        throws Exception
    {
        EnvManager.InitEnv ("");

        BoundedUniform uniformRandom = new BoundedUniform (
            0.,
            1.
        );

        R1Uniform uniformDistribution = new R1Uniform (
            0.,
            1.
        );

        int[] aiSampleSize = new int[] {
            50, 500, 5000, 50000, 500000, 5000000, 50000000
        };

        double[] adblTolerance = new double[] {
            0.01, 0.03, 0.05, 0.07, 0.10
        };

        Head ("\t|         WEAK LAW OF LARGE NUMBERS     -      METRICS FROM UNDERLYING GENERATOR        |");

        WeakLawBounds (
            uniformRandom,
            uniformDistribution,
            aiSampleSize,
            adblTolerance
        );

        System.out.println ("\t|---------------------------------------------------------------------------------------|");

        Head ("\t|        WEAK LAW OF LARGE NUMBERS      -     METRICS FROM EMPIRICAL DISTRIBUTION       |");

        WeakLawBounds (
            uniformRandom,
            null,
            aiSampleSize,
            adblTolerance
        );

        System.out.println ("\t|---------------------------------------------------------------------------------------|");

        Head ("\t|         CHERNOFF-HOEFFDING BOUNDS      -     METRICS FROM UNDERLYING GENERATOR        |");

        ChernoffHoeffdingBounds (
            uniformRandom,
            uniformDistribution,
            uniformRandom.upperBound() - uniformRandom.lowerBound(),
            aiSampleSize,
            adblTolerance
        );

        System.out.println ("\t|---------------------------------------------------------------------------------------|");

        Head ("\t|         CHERNOFF-HOEFFDING BOUNDS      -     METRICS FROM EMPIRICAL DISTRIBUTION      |");

        ChernoffHoeffdingBounds (
            uniformRandom,
            null,
            uniformRandom.upperBound() - uniformRandom.lowerBound(),
            aiSampleSize,
            adblTolerance
        );

        System.out.println ("\t|---------------------------------------------------------------------------------------|");

        Head ("\t|              BENNETT BOUNDS      -      METRICS FROM UNDERLYING GENERATOR             |");

        BennettBounds (
            uniformRandom,
            uniformDistribution,
            uniformRandom.upperBound() - uniformRandom.lowerBound(),
            aiSampleSize,
            adblTolerance
        );

        System.out.println ("\t|---------------------------------------------------------------------------------------|");

        Head ("\t|              BENNETT BOUNDS      -      METRICS FROM EMPIRICAL DISTRIBUTION           |");

        BennettBounds (
            uniformRandom,
            null,
            uniformRandom.upperBound() - uniformRandom.lowerBound(),
            aiSampleSize,
            adblTolerance
        );

        System.out.println ("\t|---------------------------------------------------------------------------------------|");

        Head ("\t|             BERNSTEIN BOUNDS      -      METRICS FROM UNDERLYING GENERATOR            |");

        BernsteinBounds (
            uniformRandom,
            uniformDistribution,
            uniformRandom.upperBound() - uniformRandom.lowerBound(),
            aiSampleSize,
            adblTolerance
        );

        System.out.println ("\t|---------------------------------------------------------------------------------------|");

        Head ("\t|            BERNSTEIN BOUNDS      -      METRICS FROM EMPIRICAL DISTRIBUTION           |");

        BernsteinBounds (
            uniformRandom,
            uniformDistribution,
            uniformRandom.upperBound() - uniformRandom.lowerBound(),
            aiSampleSize,
            adblTolerance
        );

        System.out.println ("\t|---------------------------------------------------------------------------------------|");
    }
}