/*
    * Licensed to the Apache Software Foundation (ASF) under one or more
    * contributor license agreements.  See the NOTICE file distributed with
    * this work for additional information regarding copyright ownership.
    * The ASF licenses this file to You 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
    *
    *      https://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.
   */
  
  /*
   * This is not the original file distributed by the Apache Software Foundation
   * It has been modified by the Hipparchus project
   */
  
  package org.hipparchus.distribution.continuous;
  
  import org.hipparchus.exception.MathIllegalArgumentException;
  import org.junit.Assert;
  import org.junit.Test;
  
  /**
   * Test cases for {@link ParetoDistribution}.
   */
  public class ParetoDistributionTest extends RealDistributionAbstractTest {
  
      //-------------- Implementations for abstract methods -----------------------
  
      /** Creates the default real distribution instance to use in tests. */
      @Override
      public ParetoDistribution makeDistribution() {
          return new ParetoDistribution(2.1, 1.4);
      }
  
      /** Creates the default cumulative probability distribution test input values */
      @Override
      public double[] makeCumulativeTestPoints() {
          // quantiles computed using R
          return new double[] { -2.226325228634938, -1.156887023657177, -0.643949578356075, -0.2027950777320613, 0.305827808237559,
                                +6.42632522863494, 5.35688702365718, 4.843949578356074, 4.40279507773206, 3.89417219176244 };
      }
  
      /** Creates the default cumulative probability density test expected values */
      @Override
      public double[] makeCumulativeTestValues() {
          return new double[] { 0, 0, 0, 0, 0, 0.791089998892, 0.730456085931, 0.689667290488, 0.645278794701, 0.578763688757 };
      }
  
      /** Creates the default probability density test expected values */
      @Override
      public double[] makeDensityTestValues() {
          return new double[] { 0, 0, 0, 0, 0, 0.0455118580441, 0.070444173646, 0.0896924681582, 0.112794186114, 0.151439332084 };
      }
  
      /**
       * Creates the default inverse cumulative probability distribution test input values.
       */
      @Override
      public double[] makeInverseCumulativeTestPoints() {
          // Exclude the test points less than zero, as they have cumulative
          // probability of zero, meaning the inverse returns zero, and not the
          // points less than zero.
          double[] points = makeCumulativeTestValues();
          double[] points2 = new double[points.length - 5];
          System.arraycopy(points, 5, points2, 0, points.length - 5);
          return points2;
      }
  
      /**
       * Creates the default inverse cumulative probability test expected values.
       */
      @Override
      public double[] makeInverseCumulativeTestValues() {
          // Exclude the test points less than zero, as they have cumulative
          // probability of zero, meaning the inverse returns zero, and not the
          // points less than zero.
          double[] points = makeCumulativeTestPoints();
          double[] points2 = new double[points.length - 5];
          System.arraycopy(points, 5, points2, 0, points.length - 5);
          return points2;
      }
  
      // --------------------- Override tolerance  --------------
      @Override
      public void setUp() {
          super.setUp();
          setTolerance(1e-9);
      }
  
      //---------------------------- Additional test cases -------------------------
  
      private void verifyQuantiles() {
         ParetoDistribution distribution = (ParetoDistribution)getDistribution();
         double mu = distribution.getScale();
         double sigma = distribution.getShape();
         setCumulativeTestPoints( new double[] { mu - 2 *sigma,  mu - sigma,
                                                 mu,             mu + sigma,
                                                 mu + 2 * sigma, mu + 3 * sigma,
                                                 mu + 4 * sigma, mu + 5 * sigma });
         verifyCumulativeProbabilities();
     }
 
     @Test
     public void testQuantiles() {
         setCumulativeTestValues(new double[] {0, 0, 0, 0.510884134236, 0.694625688662, 0.785201995008, 0.837811522357, 0.871634279326});
         setDensityTestValues(new double[] {0, 0, 0.666666666, 0.195646346305, 0.0872498032394, 0.0477328899983, 0.0294888141169, 0.0197485724114});
         verifyQuantiles();
         verifyDensities();
 
         setDistribution(new ParetoDistribution(1, 1));
         setCumulativeTestValues(new double[] {0, 0, 0, 0.5, 0.666666666667, 0.75, 0.8, 0.833333333333});
         setDensityTestValues(new double[] {0, 0, 1.0, 0.25, 0.111111111111, 0.0625, 0.04, 0.0277777777778});
         verifyQuantiles();
         verifyDensities();
 
         setDistribution(new ParetoDistribution(0.1, 0.1));
         setCumulativeTestValues(new double[] {0, 0, 0, 0.0669670084632, 0.104041540159, 0.129449436704, 0.148660077479, 0.164041197922});
         setDensityTestValues(new double[] {0, 0, 1.0, 0.466516495768, 0.298652819947, 0.217637640824, 0.170267984504, 0.139326467013});
         verifyQuantiles();
         verifyDensities();
     }
 
     @Test
     public void testInverseCumulativeProbabilityExtremes() {
         setInverseCumulativeTestPoints(new double[] {0, 1});
         setInverseCumulativeTestValues(new double[] {2.1, Double.POSITIVE_INFINITY});
         verifyInverseCumulativeProbabilities();
     }
 
     @Test
     public void testGetScale() {
         ParetoDistribution distribution = (ParetoDistribution)getDistribution();
         Assert.assertEquals(2.1, distribution.getScale(), 0);
     }
 
     @Test
     public void testGetShape() {
         ParetoDistribution distribution = (ParetoDistribution)getDistribution();
         Assert.assertEquals(1.4, distribution.getShape(), 0);
     }
 
     @Test(expected=MathIllegalArgumentException.class)
     public void testPreconditions() {
         new ParetoDistribution(1, 0);
     }
 
     @Test
     public void testDensity() {
         double [] x = new double[]{-2, -1, 0, 1, 2};
         // R 2.14: print(dpareto(c(-2,-1,0,1,2), scale=1, shape=1), digits=10)
         checkDensity(1, 1, x, new double[] { 0.00, 0.00, 0.00, 1.00, 0.25 });
         // R 2.14: print(dpareto(c(-2,-1,0,1,2), scale=1.1, shape=1), digits=10)
         checkDensity(1.1, 1, x, new double[] { 0.000, 0.000, 0.000, 0.000, 0.275 });
     }
 
     private void checkDensity(double scale, double shape, double[] x,
         double[] expected) {
         ParetoDistribution d = new ParetoDistribution(scale, shape);
         for (int i = 0; i < x.length; i++) {
             Assert.assertEquals(expected[i], d.density(x[i]), 1e-9);
         }
     }
 
     /**
      * Check to make sure top-coding of extreme values works correctly.
      */
     @Test
     public void testExtremeValues() {
         ParetoDistribution d = new ParetoDistribution(1, 1);
         for (int i = 0; i < 1e5; i++) { // make sure no convergence exception
             double upperTail = d.cumulativeProbability(i);
             if (i <= 1000) { // make sure not top-coded
                 Assert.assertTrue(upperTail < 1.0d);
             }
             else { // make sure top coding not reversed
                 Assert.assertTrue(upperTail > 0.999);
             }
         }
 
         Assert.assertEquals(d.cumulativeProbability(Double.MAX_VALUE), 1, 0);
         Assert.assertEquals(d.cumulativeProbability(-Double.MAX_VALUE), 0, 0);
         Assert.assertEquals(d.cumulativeProbability(Double.POSITIVE_INFINITY), 1, 0);
         Assert.assertEquals(d.cumulativeProbability(Double.NEGATIVE_INFINITY), 0, 0);
     }
 
     @Test
     public void testMeanVariance() {
         final double tol = 1e-9;
         ParetoDistribution dist;
 
         dist = new ParetoDistribution(1, 1);
         Assert.assertEquals(dist.getNumericalMean(), Double.POSITIVE_INFINITY, tol);
         Assert.assertEquals(dist.getNumericalVariance(), Double.POSITIVE_INFINITY, tol);
 
         dist = new ParetoDistribution(2.2, 2.4);
         Assert.assertEquals(dist.getNumericalMean(), 3.771428571428, tol);
         Assert.assertEquals(dist.getNumericalVariance(), 14.816326530, tol);
     }
 }