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    * Licensed to the Apache Software Foundation (ASF) under one or more
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    * 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.
   */
  
  package org.apache.commons.statistics.distribution;
  
  import java.util.stream.IntStream;
  import java.util.stream.Stream;
  import org.apache.commons.numbers.core.Precision;
  import org.apache.commons.rng.simple.RandomSource;
  import org.junit.jupiter.api.Assertions;
  import org.junit.jupiter.api.Test;
  import org.junit.jupiter.params.ParameterizedTest;
  import org.junit.jupiter.params.provider.Arguments;
  import org.junit.jupiter.params.provider.CsvSource;
  import org.junit.jupiter.params.provider.MethodSource;
  
  /**
   * Test cases for {@link HypergeometricDistribution}.
   * Extends {@link BaseDiscreteDistributionTest}. See javadoc of that class for details.
   */
  class HypergeometricDistributionTest extends BaseDiscreteDistributionTest {
      @Override
      DiscreteDistribution makeDistribution(Object... parameters) {
          final int populationSize = (Integer) parameters[0];
          final int numberOfSuccesses = (Integer) parameters[1];
          final int sampleSize = (Integer) parameters[2];
          return HypergeometricDistribution.of(populationSize, numberOfSuccesses, sampleSize);
      }
  
      @Override
      Object[][] makeInvalidParameters() {
          return new Object[][] {
              {0, 3, 5},
              {-1, 3, 5},
              {5, -1, 5},
              {5, 3, -1},
              {5, 6, 5},
              {5, 3, 6},
          };
      }
  
      @Override
      String[] getParameterNames() {
          return new String[] {"PopulationSize", "NumberOfSuccesses", "SampleSize"};
      }
  
      @Override
      protected double getRelativeTolerance() {
          return 5e-15;
      }
  
      //-------------------- Additional test cases -------------------------------
  
      @ParameterizedTest
      @MethodSource
      void testAdditionalMoments(int populationSize,
                                 int numberOfSuccesses,
                                 int sampleSize,
                                 double mean, double variance) {
          final HypergeometricDistribution dist = HypergeometricDistribution.of(populationSize, numberOfSuccesses, sampleSize);
          testMoments(dist, mean, variance, DoubleTolerances.ulps(1));
      }
  
      static Stream<Arguments> testAdditionalMoments() {
          return Stream.of(
              Arguments.of(1500, 40, 100, 40d * 100d / 1500d, (100d * 40d * (1500d - 100d) * (1500d - 40d)) / (1500d * 1500d * 1499d)),
              Arguments.of(3000, 55, 200, 55d * 200d / 3000d, (200d * 55d * (3000d - 200d) * (3000d - 55d)) / (3000d * 3000d * 2999d))
          );
      }
  
      @Test
      void testLargeValues() {
          final int populationSize = 3456;
          final int sampleSize = 789;
          final int numberOfSucceses = 101;
          // data[i][3] contains P(x >= x).
          // It is tested using survivalProbability(x - 1)
          final double[][] data = {
              {0.0, 2.75646034603961e-12, 2.75646034603961e-12, 1.0},
              {1.0, 8.55705370142386e-11, 8.83269973602783e-11, 0.999999999997244},
              {2.0, 1.31288129219665e-9, 1.40120828955693e-9, 0.999999999911673},
              {3.0, 1.32724172984193e-8, 1.46736255879763e-8, 0.999999998598792},
              {4.0, 9.94501711734089e-8, 1.14123796761385e-7, 0.999999985326375},
              {5.0, 5.89080768883643e-7, 7.03204565645028e-7, 0.999999885876203},
              {20.0, 0.0760051397707708, 0.27349758476299, 0.802507555007781},
             {21.0, 0.087144222047629, 0.360641806810619, 0.72650241523701},
             {22.0, 0.0940378846881819, 0.454679691498801, 0.639358193189381},
             {23.0, 0.0956897500614809, 0.550369441560282, 0.545320308501199},
             {24.0, 0.0919766921922999, 0.642346133752582, 0.449630558439718},
             {25.0, 0.083641637261095, 0.725987771013677, 0.357653866247418},
             {96.0, 5.93849188852098e-57, 1.0, 6.01900244560712e-57},
             {97.0, 7.96593036832547e-59, 1.0, 8.05105570861321e-59},
             {98.0, 8.44582921934367e-61, 1.0, 8.5125340287733e-61},
             {99.0, 6.63604297068222e-63, 1.0, 6.670480942963e-63},
             {100.0, 3.43501099007557e-65, 1.0, 3.4437972280786e-65},
             {101.0, 8.78623800302957e-68, 1.0, 8.78623800302957e-68},
             // Out of domain
             {sampleSize + 1, 0, 1.0, 0},
         };
 
         testHypergeometricDistributionProbabilities(populationSize, sampleSize, numberOfSucceses, data);
     }
 
     private static void testHypergeometricDistributionProbabilities(int populationSize, int sampleSize,
         int numberOfSuccesses, double[][] data) {
         final HypergeometricDistribution dist = HypergeometricDistribution.of(populationSize, numberOfSuccesses, sampleSize);
         for (int i = 0; i < data.length; ++i) {
             final int x = (int)data[i][0];
             final double pmf = data[i][1];
             final double actualPmf = dist.probability(x);
             TestUtils.assertRelativelyEquals(() -> "Expected equals for <" + x + "> pmf", pmf, actualPmf, 1.0e-9);
 
             final double cdf = data[i][2];
             final double actualCdf = dist.cumulativeProbability(x);
             TestUtils.assertRelativelyEquals(() -> "Expected equals for <" + x + "> cdf", cdf, actualCdf, 1.0e-9);
 
             final double cdf1 = data[i][3];
             final double actualCdf1 = dist.survivalProbability(x - 1);
             TestUtils.assertRelativelyEquals(() -> "Expected equals for <" + x + "> cdf1", cdf1, actualCdf1, 1.0e-9);
         }
     }
 
     @Test
     void testMoreLargeValues() {
         final int populationSize = 26896;
         final int sampleSize = 895;
         final int numberOfSucceses = 55;
         final double[][] data = {
             {0.0, 0.155168304750504, 0.155168304750504, 1.0},
             {1.0, 0.29437545000746, 0.449543754757964, 0.844831695249496},
             {2.0, 0.273841321577003, 0.723385076334967, 0.550456245242036},
             {3.0, 0.166488572570786, 0.889873648905753, 0.276614923665033},
             {4.0, 0.0743969744713231, 0.964270623377076, 0.110126351094247},
             {5.0, 0.0260542785784855, 0.990324901955562, 0.0357293766229237},
             {20.0, 3.57101101678792e-16, 1.0, 3.78252101622096e-16},
             {21.0, 2.00551638598312e-17, 1.0, 2.11509999433041e-17},
             {22.0, 1.04317070180562e-18, 1.0, 1.09583608347287e-18},
             {23.0, 5.03153504903308e-20, 1.0, 5.266538166725e-20},
             {24.0, 2.2525984149695e-21, 1.0, 2.35003117691919e-21},
             {25.0, 9.3677424515947e-23, 1.0, 9.74327619496943e-23},
             {50.0, 9.83633962945521e-69, 1.0, 9.8677629437617e-69},
             {51.0, 3.13448949497553e-71, 1.0, 3.14233143064882e-71},
             {52.0, 7.82755221928122e-74, 1.0, 7.84193567329055e-74},
             {53.0, 1.43662126065532e-76, 1.0, 1.43834540093295e-76},
             {54.0, 1.72312692517348e-79, 1.0, 1.7241402776278e-79},
             {55.0, 1.01335245432581e-82, 1.0, 1.01335245432581e-82},
         };
         testHypergeometricDistributionProbabilities(populationSize, sampleSize, numberOfSucceses, data);
     }
 
     /**
      * Test Math-644 is ported from Commons Math 3 where the distribution had the function
      * upperCumulativeProbability(x) to compute P(X >= x). This has been replaced
      * in Commons Statistics with survivalProbability(x) which computes P(X > x). To
      * create the equivalent use survivalProbability(x - 1).
      */
     @Test
     void testMath644() {
         final int N = 14761461;  // population
         final int m = 1035;      // successes in population
         final int n = 1841;      // number of trials
 
         final int k = 0;
         final HypergeometricDistribution dist = HypergeometricDistribution.of(N, m, n);
 
         // Compute upper cumulative probability using the survival probability
         Assertions.assertEquals(0, Precision.compareTo(1.0, dist.survivalProbability(k - 1), 1));
         Assertions.assertTrue(Precision.compareTo(dist.cumulativeProbability(k), 0.0, 1) > 0);
 
         // another way to calculate the upper cumulative probability
         final double upper = 1.0 - dist.cumulativeProbability(k) + dist.probability(k);
         Assertions.assertEquals(0, Precision.compareTo(1.0, upper, 1));
     }
 
     @Test
     void testZeroTrials() {
         final int n = 11; // population
         final int m = 4;  // successes in population
         final int s = 0;  // number of trials
 
         final HypergeometricDistribution dist = HypergeometricDistribution.of(n, m, s);
 
         for (int i = 1; i <= n; i++) {
             final double p = dist.probability(i);
             Assertions.assertEquals(0, p, () -> "p=" + p);
         }
     }
 
     @Test
     void testMath1356() {
         final int n = 11;  // population
         final int m = 11;  // successes in population
 
         for (int s = 0; s <= n; s++) {
             final HypergeometricDistribution dist = HypergeometricDistribution.of(n, m, s);
             final double p = dist.probability(s);
             Assertions.assertEquals(1, p, () -> "p=" + p);
         }
     }
 
     @Test
     void testMath1021() {
         final int N = 43130568;
         final int m = 42976365;
         final int n = 50;
         final DiscreteDistribution.Sampler dist =
             HypergeometricDistribution.of(N, m, n).createSampler(RandomSource.XO_SHI_RO_256_PP.create());
 
         for (int i = 0; i < 100; i++) {
             final int sample = dist.sample();
             Assertions.assertTrue(0 <= sample, () -> "sample=" + sample);
             Assertions.assertTrue(sample <= n, () -> "sample=" + sample);
         }
     }
 
     @Test
     void testAdditionalCumulativeProbabilityHighPrecision() {
         // computed using R version 3.4.4
         testCumulativeProbabilityHighPrecision(
             HypergeometricDistribution.of(500, 70, 300),
             new int[] {10, 8},
             new double[] {2.4055720603264525e-17, 1.2848174992266236e-19},
             DoubleTolerances.relative(5e-14));
     }
 
     @Test
     void testAdditionalSurvivalProbabilityHighPrecision() {
         // computed using R version 3.4.4
         testSurvivalProbabilityHighPrecision(
             HypergeometricDistribution.of(500, 70, 300),
             new int[] {68, 69},
             new double[] {4.570379934029859e-16, 7.4187180434325268e-18},
             DoubleTolerances.relative(5e-14));
     }
 
     @ParameterizedTest
     @CsvSource({
         "1, 0, 0",
         "1, 1, 0",
         "1, 0, 1",
         "1, 1, 1",
         "2, 1, 1",
         "2, 1, 2",
         "2, 2, 1",
         "2, 2, 2",
         "3, 1, 1",
         "3, 1, 2",
         "3, 1, 3",
         "3, 2, 1",
         "3, 2, 2",
         "3, 2, 3",
         "3, 3, 1",
         "3, 3, 2",
         "3, 3, 3",
         // Mean = n * K / N
         "15, 9, 7", // 4.2
         "23, 13, 11", // 6.22
         "200, 130, 70", // 45.5
     })
     void testAdditionalInverseMapping(int populationSize, int numberOfSuccesses, int sampleSize) {
         final HypergeometricDistribution dist = HypergeometricDistribution.of(populationSize, numberOfSuccesses, sampleSize);
         final int[] points = IntStream.rangeClosed(dist.getSupportLowerBound(), dist.getSupportUpperBound()).toArray();
         testCumulativeProbabilityInverseMapping(dist, points);
         testSurvivalProbabilityInverseMapping(dist, points);
     }
 }