[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(https://github.com/apache/spark/pull/11108).
Since PR(https://github.com/apache/spark/pull/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 <iamshrek@126.com>

Closes #11901 from keypointt/SPARK-13019.

6 files changed, 277 insertions, 0 deletions

diff --git a/examples/src/main/python/mllib/correlations_example.py b/examples/src/main/python/mllib/correlations_example.py
new file mode 100644
index 0000000000..66d18f6e5d
--- /dev/null
+++ b/examples/src/main/python/mllib/correlations_example.py
@@ -0,0 +1,48 @@
+#
+# 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.
+#
+
+from __future__ import print_function
+
+import numpy as np
+
+from pyspark import SparkContext
+# $example on$
+from pyspark.mllib.stat import Statistics
+# $example off$
+
+if __name__ == "__main__":
+    sc = SparkContext(appName="CorrelationsExample")  # SparkContext
+
+    # $example on$
+    seriesX = sc.parallelize([1.0, 2.0, 3.0, 3.0, 5.0])  # a series
+    # seriesY must have the same number of partitions and cardinality as seriesX
+    seriesY = sc.parallelize([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.
+    print("Correlation is: " + str(Statistics.corr(seriesX, seriesY, method="pearson")))
+
+    data = sc.parallelize(
+        [np.array([1.0, 10.0, 100.0]), np.array([2.0, 20.0, 200.0]), np.array([5.0, 33.0, 366.0])]
+    )  # an RDD of Vectors
+
+    # 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.
+    print(Statistics.corr(data, method="pearson"))
+    # $example off$
+
+    sc.stop()
diff --git a/examples/src/main/python/mllib/hypothesis_testing_example.py b/examples/src/main/python/mllib/hypothesis_testing_example.py
new file mode 100644
index 0000000000..e566ead0d3
--- /dev/null
+++ b/examples/src/main/python/mllib/hypothesis_testing_example.py
@@ -0,0 +1,65 @@
+#
+# 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.
+#
+
+from __future__ import print_function
+
+from pyspark import SparkContext
+# $example on$
+from pyspark.mllib.linalg import Matrices, Vectors
+from pyspark.mllib.regression import LabeledPoint
+from pyspark.mllib.stat import Statistics
+# $example off$
+
+if __name__ == "__main__":
+    sc = SparkContext(appName="HypothesisTestingExample")
+
+    # $example on$
+    vec = Vectors.dense(0.1, 0.15, 0.2, 0.3, 0.25)  # a vector composed of the frequencies of events
+
+    # 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.
+    goodnessOfFitTestResult = Statistics.chiSqTest(vec)
+
+    # summary of the test including the p-value, degrees of freedom,
+    # test statistic, the method used, and the null hypothesis.
+    print("%s\n" % goodnessOfFitTestResult)
+
+    mat = Matrices.dense(3, 2, [1.0, 3.0, 5.0, 2.0, 4.0, 6.0])  # a contingency matrix
+
+    # conduct Pearson's independence test on the input contingency matrix
+    independenceTestResult = Statistics.chiSqTest(mat)
+
+    # summary of the test including the p-value, degrees of freedom,
+    # test statistic, the method used, and the null hypothesis.
+    print("%s\n" % independenceTestResult)
+
+    obs = sc.parallelize(
+        [LabeledPoint(1.0, [1.0, 0.0, 3.0]),
+         LabeledPoint(1.0, [1.0, 2.0, 0.0]),
+         LabeledPoint(1.0, [-1.0, 0.0, -0.5])]
+    )  # LabeledPoint(feature, label)
+
+    # The contingency table is constructed from an RDD of LabeledPoint and used to conduct
+    # the independence test. Returns an array containing the ChiSquaredTestResult for every feature
+    # against the label.
+    featureTestResults = Statistics.chiSqTest(obs)
+
+    for i, result in enumerate(featureTestResults):
+        print("Column %d:\n%s" % (i + 1, result))
+    # $example off$
+
+    sc.stop()
diff --git a/examples/src/main/python/mllib/hypothesis_testing_kolmogorov_smirnov_test_example.py b/examples/src/main/python/mllib/hypothesis_testing_kolmogorov_smirnov_test_example.py
new file mode 100644
index 0000000000..ef380dee79
--- /dev/null
+++ b/examples/src/main/python/mllib/hypothesis_testing_kolmogorov_smirnov_test_example.py
@@ -0,0 +1,40 @@
+#
+# 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.
+#
+
+from __future__ import print_function
+
+from pyspark import SparkContext
+# $example on$
+from pyspark.mllib.stat import Statistics
+# $example off$
+
+if __name__ == "__main__":
+    sc = SparkContext(appName="HypothesisTestingKolmogorovSmirnovTestExample")
+
+    # $example on$
+    parallelData = sc.parallelize([0.1, 0.15, 0.2, 0.3, 0.25])
+
+    # run a KS test for the sample versus a standard normal distribution
+    testResult = Statistics.kolmogorovSmirnovTest(parallelData, "norm", 0, 1)
+    # 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
+    # Note that the Scala functionality of calling Statistics.kolmogorovSmirnovTest with
+    # a lambda to calculate the CDF is not made available in the Python API
+    print(testResult)
+    # $example off$
+
+    sc.stop()
diff --git a/examples/src/main/python/mllib/kernel_density_estimation_example.py b/examples/src/main/python/mllib/kernel_density_estimation_example.py
new file mode 100644
index 0000000000..3e8f7241a4
--- /dev/null
+++ b/examples/src/main/python/mllib/kernel_density_estimation_example.py
@@ -0,0 +1,44 @@
+#
+# 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.
+#
+
+from __future__ import print_function
+
+from pyspark import SparkContext
+# $example on$
+from pyspark.mllib.stat import KernelDensity
+# $example off$
+
+if __name__ == "__main__":
+    sc = SparkContext(appName="KernelDensityEstimationExample")  # SparkContext
+
+    # $example on$
+    # an RDD of sample data
+    data = sc.parallelize([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
+    kd = KernelDensity()
+    kd.setSample(data)
+    kd.setBandwidth(3.0)
+
+    # Find density estimates for the given values
+    densities = kd.estimate([-1.0, 2.0, 5.0])
+    # $example off$
+
+    print(densities)
+
+    sc.stop()
diff --git a/examples/src/main/python/mllib/stratified_sampling_example.py b/examples/src/main/python/mllib/stratified_sampling_example.py
new file mode 100644
index 0000000000..a13f8f08dd
--- /dev/null
+++ b/examples/src/main/python/mllib/stratified_sampling_example.py
@@ -0,0 +1,38 @@
+#
+# 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.
+#
+
+from __future__ import print_function
+
+from pyspark import SparkContext
+
+if __name__ == "__main__":
+    sc = SparkContext(appName="StratifiedSamplingExample")  # SparkContext
+
+    # $example on$
+    # an RDD of any key value pairs
+    data = sc.parallelize([(1, 'a'), (1, 'b'), (2, 'c'), (2, 'd'), (2, 'e'), (3, 'f')])
+
+    # specify the exact fraction desired from each key as a dictionary
+    fractions = {1: 0.1, 2: 0.6, 3: 0.3}
+
+    approxSample = data.sampleByKey(False, fractions)
+    # $example off$
+
+    for each in approxSample.collect():
+        print(each)
+
+    sc.stop()
diff --git a/examples/src/main/python/mllib/summary_statistics_example.py b/examples/src/main/python/mllib/summary_statistics_example.py
new file mode 100644
index 0000000000..d55d1a2c2d
--- /dev/null
+++ b/examples/src/main/python/mllib/summary_statistics_example.py
@@ -0,0 +1,42 @@
+#
+# 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.
+#
+
+from __future__ import print_function
+
+from pyspark import SparkContext
+# $example on$
+import numpy as np
+
+from pyspark.mllib.stat import Statistics
+# $example off$
+
+if __name__ == "__main__":
+    sc = SparkContext(appName="SummaryStatisticsExample")  # SparkContext
+
+    # $example on$
+    mat = sc.parallelize(
+        [np.array([1.0, 10.0, 100.0]), np.array([2.0, 20.0, 200.0]), np.array([3.0, 30.0, 300.0])]
+    )  # an RDD of Vectors
+
+    # Compute column summary statistics.
+    summary = Statistics.colStats(mat)
+    print(summary.mean())  # a dense vector containing the mean value for each column
+    print(summary.variance())  # column-wise variance
+    print(summary.numNonzeros())  # number of nonzeros in each column
+    # $example off$
+
+    sc.stop()