PlottingPositionGeneratorFilliben.java

package org.drip.validation.quantile;

/*
 * -*- 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>PlottingPositionGeneratorFilliben</i> holds the Order Statistic Median Based Heuristic Plotting
 * Position Generation Schemes.
 *
 *  <br><br>
 *  <ul>
 *      <li>
 *          Filliben, J. J. (1975): The Probability Plot Correlation Coefficient Test for Normality
 *              <i>Technometrics, American Society for Quality</i> <b>17 (1)</b> 111-117
 *      </li>
 *      <li>
 *          Gibbons, J. D., and S. Chakraborti (2003): <i>Non-parametric Statistical Inference 4th
 *              Edition</i> <b>CRC Press</b>
 *      </li>
 *      <li>
 *          Gnanadesikan, R. (1977): <i>Methods for Statistical Analysis of Multivariate Observations</i>
 *              <b>Wiley</b>
 *      </li>
 *      <li>
 *          Thode, H. C. (2002): <i>Testing for Normality</i> <b>Marcel Dekker</b> New York
 *      </li>
 *      <li>
 *          Wikipedia (2018): Q-Q Plot https://en.wikipedia.org/wiki/Q%E2%80%93Q_plot
 *      </li>
 *  </ul>
 *
 *  <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/ModelValidationAnalyticsLibrary.md">Model Validation Analytics Library</a></li>
 *      <li><b>Project</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/src/main/java/org/drip/validation/README.md">Risk Factor and Hypothesis Validation, Evidence Processing, and Model Testing</a></li>
 *      <li><b>Package</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/src/main/java/org/drip/validation/quantile/README.md">Quantile Based Graphical Numerical Validators</a></li>
 *  </ul>
 * <br><br>
 *
 * @author Lakshmi Krishnamurthy
 */

public class PlottingPositionGeneratorFilliben extends org.drip.validation.quantile.PlottingPositionGenerator
{

    /**
     * PlottingPositionGeneratorFilliben Constructor
     * 
     * @param orderStatisticCount Count of Order Statistics
     * 
     * @throws java.lang.Exception Thrown if the Inputs are Invalid
     */

    public PlottingPositionGeneratorFilliben (
        final int orderStatisticCount)
        throws java.lang.Exception
    {
        super (orderStatisticCount);
    }

    @Override public org.drip.validation.quantile.PlottingPosition[] generate()
    {
        int orderStatisticCount = orderStatisticCount();

        org.drip.validation.quantile.PlottingPosition[] plottingPositionArray = new
            org.drip.validation.quantile.PlottingPosition[orderStatisticCount];

        double terminalQuantile = java.lang.Math.pow (
            0.5,
            1. / orderStatisticCount
        );

        try
        {
            plottingPositionArray[0] = new org.drip.validation.quantile.PlottingPosition (
                1,
                1. - terminalQuantile
            );

            plottingPositionArray[orderStatisticCount - 1] =
                new org.drip.validation.quantile.PlottingPosition (
                    orderStatisticCount,
                    terminalQuantile
                );
        }
        catch (java.lang.Exception e)
        {
            e.printStackTrace();

            return null;
        }

        for (int orderStatisticIndex = 2; orderStatisticIndex < orderStatisticCount; ++orderStatisticIndex)
        {
            try
            {
                plottingPositionArray[orderStatisticIndex - 1] =
                    new org.drip.validation.quantile.PlottingPosition (
                        orderStatisticIndex,
                        (((double) orderStatisticIndex) - 0.3175) / (0.365 + orderStatisticCount)
                    );
            }
            catch (java.lang.Exception e)
            {
                e.printStackTrace();

                return null;
            }
        }

        return plottingPositionArray;
    }
}