MATH-1671: Update stat.descriptive package to use Commons Statistics

Removes redundant classes.

descriptive.moment:

- FirstMoment
- FourthMoment
- GeometricMean
- Kurtosis
- SecondMoment
- Skewness
- StandardDeviation
- ThirdMoment

Mean + Variance have been changed to only implement the weighted
evaluation interface.

descriptive.rank:
- Min
- Max

descriptive.summary:
- Sum
- SumOfLogs
- SumOfSquares

Product has been changed to only implement the weighted evaluation
interface.

The utility class StatUtils has been updated to delegate all calls to
Commons Statistics. Legacy Math exceptions have been preserved. Removes
methods to compute the variance using an existing mean:

public static double variance(double[] values, double mean, int begin,
int length)
public static double variance(double[] values, double mean)
public static double populationVariance(double[] values, double mean,
int begin, int length)
public static double populationVariance(double[] values, double mean)

Note: StatUtils has inconsistent documentation of what to return for an
empty array. The documentation states NaN but StatUtilsTest requires
otherwise:

Sum-of-squares = 0
Product = 1
Sum-of-logs = 0

This is inconsistent and has been updated to NaN for all statistics.

The class MultivariateSummaryStatistics has been updated with partial
implementations of StorelessUnivariateStatistic that delegate to Commons
Statistics.

Some test classes have been updated to pass the build after removal of
the statistic implementations.

Author: aherbert

commons-math-legacy/src/main/java/org/apache/commons/math4/legacy/ml/clustering/KMeansPlusPlusClusterer.java

@@ -24,10 +24,9 @@
 import org.apache.commons.math4.legacy.exception.util.LocalizedFormats;
 import org.apache.commons.math4.legacy.ml.distance.DistanceMeasure;
 import org.apache.commons.math4.legacy.ml.distance.EuclideanDistance;
-import org.apache.commons.math4.legacy.stat.descriptive.moment.Variance;
 import org.apache.commons.rng.UniformRandomProvider;
 import org.apache.commons.rng.simple.RandomSource;
-
+import org.apache.commons.statistics.descriptive.Variance;
 import java.util.ArrayList;
 import java.util.Collection;
 import java.util.Collections;
@@ -431,11 +430,11 @@ private T getPointFromLargestVarianceCluster(final Collection<CentroidCluster<T>
 
                 // compute the distance variance of the current cluster
                 final Clusterable center = cluster.getCenter();
-                final Variance stat = new Variance();
+                final Variance stat = Variance.create();
                 for (final T point : cluster.getPoints()) {
-                    stat.increment(distance(point, center));
+                    stat.accept(distance(point, center));
                 }
-                final double variance = stat.getResult();
+                final double variance = stat.getAsDouble();
 
                 // select the cluster with the largest variance
                 if (variance > maxVariance) {

commons-math-legacy/src/main/java/org/apache/commons/math4/legacy/ml/clustering/evaluation/SumOfClusterVariances.java

@@ -23,7 +23,7 @@
 import org.apache.commons.math4.legacy.ml.clustering.Clusterable;
 import org.apache.commons.math4.legacy.ml.clustering.ClusterEvaluator;
 import org.apache.commons.math4.legacy.ml.distance.DistanceMeasure;
-import org.apache.commons.math4.legacy.stat.descriptive.moment.Variance;
+import org.apache.commons.statistics.descriptive.Variance;
 
 /**
  * Computes the sum of intra-cluster distance variances according to the formula:
@@ -56,12 +56,12 @@ public double score(List<? extends Cluster<? extends Clusterable>> clusters) {
                 final Clusterable center = cluster.centroid();
 
                 // compute the distance variance of the current cluster
-                final Variance stat = new Variance();
+                final Variance stat = Variance.create();
                 for (final Clusterable point : cluster.getPoints()) {
-                    stat.increment(distance(point, center));
+                    stat.accept(distance(point, center));
                 }
 
-                varianceSum += stat.getResult();
+                varianceSum += stat.getAsDouble();
             }
         }
         return varianceSum;

commons-math-legacy/src/main/java/org/apache/commons/math4/legacy/optim/nonlinear/scalar/SimulatedAnnealing.java

@@ -19,7 +19,7 @@
 import java.util.function.BiFunction;
 import java.util.function.DoublePredicate;
 import org.apache.commons.rng.UniformRandomProvider;
-import org.apache.commons.math4.legacy.stat.descriptive.moment.StandardDeviation;
+import org.apache.commons.statistics.descriptive.StandardDeviation;
 import org.apache.commons.math4.legacy.optim.OptimizationData;
 import org.apache.commons.math4.legacy.optim.nonlinear.scalar.noderiv.Simplex;
 
@@ -164,11 +164,11 @@ static CoolingSchedule aarstAndVanLaarhoven(final double delta) {
 
             return (previousTemperature, simplex) -> {
                 // Standard deviation of the values of the objective function.
-                final StandardDeviation stddev = new StandardDeviation();
+                final StandardDeviation stddev = StandardDeviation.create();
                 for (int i = 0; i < simplex.getSize(); i++) {
-                    stddev.increment(simplex.get(i).getValue());
+                    stddev.accept(simplex.get(i).getValue());
                 }
-                final double sigma = stddev.getResult();
+                final double sigma = stddev.getAsDouble();
 
                 final double a = previousTemperature * Math.log(1 + delta);
                 final double b = 3 * sigma;