[SPARK-13019][DOCS] fix for scala-2.10 build: Replace example code in mllib-statistics.md using include_example

## What changes were proposed in this pull request?

This PR for ticket SPARK-13019 is based on previous PR(#11108).
Since PR(#11108) is breaking scala-2.10 build, more work is needed to fix build errors.

What I did new in this PR is adding keyword argument for 'fractions':
`    val approxSample = data.sampleByKey(withReplacement = false, fractions = fractions)`
`    val exactSample = data.sampleByKeyExact(withReplacement = false, fractions = fractions)`

I reopened ticket on JIRA but sorry I don't know how to reopen a GitHub pull request, so I just submitting a new pull request.
## How was this patch tested?

Manual build testing on local machine, build based on scala-2.10.

Author: Xin Ren <[email protected]>

Closes #11901 from keypointt/SPARK-13019.

Author: keypointt

docs/mllib-statistics.md

@@ -0,0 +1,70 @@
+/*
+ * 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
+ *
+ *    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.
+ */
+
+package org.apache.spark.examples.mllib;
+
+import org.apache.spark.SparkConf;
+import org.apache.spark.api.java.JavaSparkContext;
+// $example on$
+import java.util.Arrays;
+
+import org.apache.spark.api.java.JavaDoubleRDD;
+import org.apache.spark.api.java.JavaRDD;
+import org.apache.spark.mllib.linalg.Matrix;
+import org.apache.spark.mllib.linalg.Vector;
+import org.apache.spark.mllib.linalg.Vectors;
+import org.apache.spark.mllib.stat.Statistics;
+// $example off$
+
+public class JavaCorrelationsExample {
+  public static void main(String[] args) {
+
+    SparkConf conf = new SparkConf().setAppName("JavaCorrelationsExample");
+    JavaSparkContext jsc = new JavaSparkContext(conf);
+
+    // $example on$
+    JavaDoubleRDD seriesX = jsc.parallelizeDoubles(
+      Arrays.asList(1.0, 2.0, 3.0, 3.0, 5.0));  // a series
+
+    // must have the same number of partitions and cardinality as seriesX
+    JavaDoubleRDD seriesY = jsc.parallelizeDoubles(
+      Arrays.asList(11.0, 22.0, 33.0, 33.0, 555.0));
+
+    // compute the correlation using Pearson's method. Enter "spearman" for Spearman's method.
+    // If a method is not specified, Pearson's method will be used by default.
+    Double correlation = Statistics.corr(seriesX.srdd(), seriesY.srdd(), "pearson");
+    System.out.println("Correlation is: " + correlation);
+
+    // note that each Vector is a row and not a column
+    JavaRDD<Vector> data = jsc.parallelize(
+      Arrays.asList(
+        Vectors.dense(1.0, 10.0, 100.0),
+        Vectors.dense(2.0, 20.0, 200.0),
+        Vectors.dense(5.0, 33.0, 366.0)
+      )
+    );
+
+    // calculate the correlation matrix using Pearson's method. Use "spearman" for Spearman's method.
+    // If a method is not specified, Pearson's method will be used by default.
+    Matrix correlMatrix = Statistics.corr(data.rdd(), "pearson");
+    System.out.println(correlMatrix.toString());
+    // $example off$
+
+    jsc.stop();
+  }
+}
+

examples/src/main/java/org/apache/spark/examples/mllib/JavaCorrelationsExample.java

@@ -0,0 +1,84 @@
+/*
+ * 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
+ *
+ *    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.
+ */
+
+package org.apache.spark.examples.mllib;
+
+import org.apache.spark.SparkConf;
+import org.apache.spark.api.java.JavaSparkContext;
+
+// $example on$
+import java.util.Arrays;
+
+import org.apache.spark.api.java.JavaRDD;
+import org.apache.spark.mllib.linalg.Matrices;
+import org.apache.spark.mllib.linalg.Matrix;
+import org.apache.spark.mllib.linalg.Vector;
+import org.apache.spark.mllib.linalg.Vectors;
+import org.apache.spark.mllib.regression.LabeledPoint;
+import org.apache.spark.mllib.stat.Statistics;
+import org.apache.spark.mllib.stat.test.ChiSqTestResult;
+// $example off$
+
+public class JavaHypothesisTestingExample {
+  public static void main(String[] args) {
+
+    SparkConf conf = new SparkConf().setAppName("JavaHypothesisTestingExample");
+    JavaSparkContext jsc = new JavaSparkContext(conf);
+
+    // $example on$
+    // a vector composed of the frequencies of events
+    Vector vec = Vectors.dense(0.1, 0.15, 0.2, 0.3, 0.25);
+
+    // compute the goodness of fit. If a second vector to test against is not supplied
+    // as a parameter, the test runs against a uniform distribution.
+    ChiSqTestResult goodnessOfFitTestResult = Statistics.chiSqTest(vec);
+    // summary of the test including the p-value, degrees of freedom, test statistic,
+    // the method used, and the null hypothesis.
+    System.out.println(goodnessOfFitTestResult + "\n");
+
+    // Create a contingency matrix ((1.0, 2.0), (3.0, 4.0), (5.0, 6.0))
+    Matrix mat = Matrices.dense(3, 2, new double[]{1.0, 3.0, 5.0, 2.0, 4.0, 6.0});
+
+    // conduct Pearson's independence test on the input contingency matrix
+    ChiSqTestResult independenceTestResult = Statistics.chiSqTest(mat);
+    // summary of the test including the p-value, degrees of freedom...
+    System.out.println(independenceTestResult + "\n");
+
+    // an RDD of labeled points
+    JavaRDD<LabeledPoint> obs = jsc.parallelize(
+      Arrays.asList(
+        new LabeledPoint(1.0, Vectors.dense(1.0, 0.0, 3.0)),
+        new LabeledPoint(1.0, Vectors.dense(1.0, 2.0, 0.0)),
+        new LabeledPoint(-1.0, Vectors.dense(-1.0, 0.0, -0.5))
+      )
+    );
+
+    // The contingency table is constructed from the raw (feature, label) pairs and used to conduct
+    // the independence test. Returns an array containing the ChiSquaredTestResult for every feature
+    // against the label.
+    ChiSqTestResult[] featureTestResults = Statistics.chiSqTest(obs.rdd());
+    int i = 1;
+    for (ChiSqTestResult result : featureTestResults) {
+      System.out.println("Column " + i + ":");
+      System.out.println(result + "\n");  // summary of the test
+      i++;
+    }
+    // $example off$
+
+    jsc.stop();
+  }
+}

examples/src/main/java/org/apache/spark/examples/mllib/JavaHypothesisTestingExample.java

@@ -0,0 +1,49 @@
+/*
+ * 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
+ *
+ *    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.
+ */
+
+package org.apache.spark.examples.mllib;
+
+import org.apache.spark.SparkConf;
+import org.apache.spark.api.java.JavaSparkContext;
+// $example on$
+import java.util.Arrays;
+
+import org.apache.spark.api.java.JavaDoubleRDD;
+import org.apache.spark.mllib.stat.Statistics;
+import org.apache.spark.mllib.stat.test.KolmogorovSmirnovTestResult;
+// $example off$
+
+public class JavaHypothesisTestingKolmogorovSmirnovTestExample {
+  public static void main(String[] args) {
+
+    SparkConf conf =
+      new SparkConf().setAppName("JavaHypothesisTestingKolmogorovSmirnovTestExample");
+    JavaSparkContext jsc = new JavaSparkContext(conf);
+
+    // $example on$
+    JavaDoubleRDD data = jsc.parallelizeDoubles(Arrays.asList(0.1, 0.15, 0.2, 0.3, 0.25));
+    KolmogorovSmirnovTestResult testResult =
+      Statistics.kolmogorovSmirnovTest(data, "norm", 0.0, 1.0);
+    // summary of the test including the p-value, test statistic, and null hypothesis
+    // if our p-value indicates significance, we can reject the null hypothesis
+    System.out.println(testResult);
+    // $example off$
+
+    jsc.stop();
+  }
+}
+

examples/src/main/java/org/apache/spark/examples/mllib/JavaHypothesisTestingKolmogorovSmirnovTestExample.java

@@ -0,0 +1,53 @@
+/*
+ * 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
+ *
+ *    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.
+ */
+
+package org.apache.spark.examples.mllib;
+
+import org.apache.spark.SparkConf;
+import org.apache.spark.api.java.JavaSparkContext;
+// $example on$
+import java.util.Arrays;
+
+import org.apache.spark.api.java.JavaRDD;
+import org.apache.spark.mllib.stat.KernelDensity;
+// $example off$
+
+public class JavaKernelDensityEstimationExample {
+  public static void main(String[] args) {
+
+    SparkConf conf = new SparkConf().setAppName("JavaKernelDensityEstimationExample");
+    JavaSparkContext jsc = new JavaSparkContext(conf);
+
+    // $example on$
+    // an RDD of sample data
+    JavaRDD<Double> data = jsc.parallelize(
+      Arrays.asList(1.0, 1.0, 1.0, 2.0, 3.0, 4.0, 5.0, 5.0, 6.0, 7.0, 8.0, 9.0, 9.0));
+
+    // Construct the density estimator with the sample data
+    // and a standard deviation for the Gaussian kernels
+    KernelDensity kd = new KernelDensity().setSample(data).setBandwidth(3.0);
+
+    // Find density estimates for the given values
+    double[] densities = kd.estimate(new double[]{-1.0, 2.0, 5.0});
+
+    System.out.println(Arrays.toString(densities));
+    // $example off$
+
+    jsc.stop();
+  }
+}
+

examples/src/main/java/org/apache/spark/examples/mllib/JavaKernelDensityEstimationExample.java

@@ -0,0 +1,75 @@
+/*
+ * 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
+ *
+ *    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.
+ */
+
+package org.apache.spark.examples.mllib;
+
+import com.google.common.collect.ImmutableMap;
+import org.apache.spark.SparkConf;
+import org.apache.spark.api.java.JavaSparkContext;
+
+// $example on$
+import java.util.*;
+
+import scala.Tuple2;
+
+import org.apache.spark.api.java.JavaPairRDD;
+import org.apache.spark.api.java.function.VoidFunction;
+// $example off$
+
+public class JavaStratifiedSamplingExample {
+  public static void main(String[] args) {
+
+    SparkConf conf = new SparkConf().setAppName("JavaStratifiedSamplingExample");
+    JavaSparkContext jsc = new JavaSparkContext(conf);
+
+    // $example on$
+    List<Tuple2<Integer, Character>> list = new ArrayList<Tuple2<Integer, Character>>(
+      Arrays.<Tuple2<Integer, Character>>asList(
+        new Tuple2(1, 'a'),
+        new Tuple2(1, 'b'),
+        new Tuple2(2, 'c'),
+        new Tuple2(2, 'd'),
+        new Tuple2(2, 'e'),
+        new Tuple2(3, 'f')
+      )
+    );
+
+    JavaPairRDD<Integer, Character> data = jsc.parallelizePairs(list);
+
+    // specify the exact fraction desired from each key Map<K, Object>
+    ImmutableMap<Integer, Object> fractions =
+      ImmutableMap.of(1, (Object)0.1, 2, (Object) 0.6, 3, (Object) 0.3);
+
+    // Get an approximate sample from each stratum
+    JavaPairRDD<Integer, Character> approxSample = data.sampleByKey(false, fractions);
+    // Get an exact sample from each stratum
+    JavaPairRDD<Integer, Character> exactSample = data.sampleByKeyExact(false, fractions);
+    // $example off$
+
+    System.out.println("approxSample size is " + approxSample.collect().size());
+    for (Tuple2<Integer, Character> t : approxSample.collect()) {
+      System.out.println(t._1() + " " + t._2());
+    }
+
+    System.out.println("exactSample size is " + exactSample.collect().size());
+    for (Tuple2<Integer, Character> t : exactSample.collect()) {
+      System.out.println(t._1() + " " + t._2());
+    }
+
+    jsc.stop();
+  }
+}

examples/src/main/java/org/apache/spark/examples/mllib/JavaStratifiedSamplingExample.java

@@ -0,0 +1,56 @@
+/*
+ * 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
+ *
+ *    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.
+ */
+
+package org.apache.spark.examples.mllib;
+
+import org.apache.spark.SparkConf;
+import org.apache.spark.api.java.JavaSparkContext;
+// $example on$
+import java.util.Arrays;
+
+import org.apache.spark.api.java.JavaRDD;
+import org.apache.spark.mllib.linalg.Vector;
+import org.apache.spark.mllib.linalg.Vectors;
+import org.apache.spark.mllib.stat.MultivariateStatisticalSummary;
+import org.apache.spark.mllib.stat.Statistics;
+// $example off$
+
+public class JavaSummaryStatisticsExample {
+  public static void main(String[] args) {
+
+    SparkConf conf = new SparkConf().setAppName("JavaSummaryStatisticsExample");
+    JavaSparkContext jsc = new JavaSparkContext(conf);
+
+    // $example on$
+    JavaRDD<Vector> mat = jsc.parallelize(
+      Arrays.asList(
+        Vectors.dense(1.0, 10.0, 100.0),
+        Vectors.dense(2.0, 20.0, 200.0),
+        Vectors.dense(3.0, 30.0, 300.0)
+      )
+    ); // an RDD of Vectors
+
+    // Compute column summary statistics.
+    MultivariateStatisticalSummary summary = Statistics.colStats(mat.rdd());
+    System.out.println(summary.mean());  // a dense vector containing the mean value for each column
+    System.out.println(summary.variance());  // column-wise variance
+    System.out.println(summary.numNonzeros());  // number of nonzeros in each column
+    // $example off$
+
+    jsc.stop();
+  }
+}