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 title: Basic Statistics - RDD-based API
 displayTitle: Basic Statistics - RDD-based API
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 * Table of contents
 {:toc}
 
 
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 ## Summary statistics
 
 We provide column summary statistics for `RDD[Vector]` through the function `colStats`
 available in `Statistics`.
 
 <div class="codetabs">
 <div data-lang="scala" markdown="1">
 
 [`colStats()`](api/scala/org/apache/spark/mllib/stat/Statistics$.html) returns an instance of
 [`MultivariateStatisticalSummary`](api/scala/org/apache/spark/mllib/stat/MultivariateStatisticalSummary.html),
 which contains the column-wise max, min, mean, variance, and number of nonzeros, as well as the
 total count.
 
 Refer to the [`MultivariateStatisticalSummary` Scala docs](api/scala/org/apache/spark/mllib/stat/MultivariateStatisticalSummary.html) for details on the API.
 
 {% include_example scala/org/apache/spark/examples/mllib/SummaryStatisticsExample.scala %}
 </div>
 
 <div data-lang="java" markdown="1">
 
 [`colStats()`](api/java/org/apache/spark/mllib/stat/Statistics.html) returns an instance of
 [`MultivariateStatisticalSummary`](api/java/org/apache/spark/mllib/stat/MultivariateStatisticalSummary.html),
 which contains the column-wise max, min, mean, variance, and number of nonzeros, as well as the
 total count.
 
 Refer to the [`MultivariateStatisticalSummary` Java docs](api/java/org/apache/spark/mllib/stat/MultivariateStatisticalSummary.html) for details on the API.
 
 {% include_example java/org/apache/spark/examples/mllib/JavaSummaryStatisticsExample.java %}
 </div>
 
 <div data-lang="python" markdown="1">
 [`colStats()`](api/python/pyspark.mllib.html#pyspark.mllib.stat.Statistics.colStats) returns an instance of
 [`MultivariateStatisticalSummary`](api/python/pyspark.mllib.html#pyspark.mllib.stat.MultivariateStatisticalSummary),
 which contains the column-wise max, min, mean, variance, and number of nonzeros, as well as the
 total count.
 
 Refer to the [`MultivariateStatisticalSummary` Python docs](api/python/pyspark.mllib.html#pyspark.mllib.stat.MultivariateStatisticalSummary) for more details on the API.
 
 {% include_example python/mllib/summary_statistics_example.py %}
 </div>
 
 </div>
 
 ## Correlations
 
 Calculating the correlation between two series of data is a common operation in Statistics. In `spark.mllib`
 we provide the flexibility to calculate pairwise correlations among many series. The supported
 correlation methods are currently Pearson's and Spearman's correlation.
 
 <div class="codetabs">
 <div data-lang="scala" markdown="1">
 [`Statistics`](api/scala/org/apache/spark/mllib/stat/Statistics$.html) provides methods to
 calculate correlations between series. Depending on the type of input, two `RDD[Double]`s or
 an `RDD[Vector]`, the output will be a `Double` or the correlation `Matrix` respectively.
 
 Refer to the [`Statistics` Scala docs](api/scala/org/apache/spark/mllib/stat/Statistics$.html) for details on the API.
 
 {% include_example scala/org/apache/spark/examples/mllib/CorrelationsExample.scala %}
 </div>
 
 <div data-lang="java" markdown="1">
 [`Statistics`](api/java/org/apache/spark/mllib/stat/Statistics.html) provides methods to
 calculate correlations between series. Depending on the type of input, two `JavaDoubleRDD`s or
 a `JavaRDD<Vector>`, the output will be a `Double` or the correlation `Matrix` respectively.
 
 Refer to the [`Statistics` Java docs](api/java/org/apache/spark/mllib/stat/Statistics.html) for details on the API.
 
 {% include_example java/org/apache/spark/examples/mllib/JavaCorrelationsExample.java %}
 </div>
 
 <div data-lang="python" markdown="1">
 [`Statistics`](api/python/pyspark.mllib.html#pyspark.mllib.stat.Statistics) provides methods to
 calculate correlations between series. Depending on the type of input, two `RDD[Double]`s or
 an `RDD[Vector]`, the output will be a `Double` or the correlation `Matrix` respectively.
 
 Refer to the [`Statistics` Python docs](api/python/pyspark.mllib.html#pyspark.mllib.stat.Statistics) for more details on the API.
 
 {% include_example python/mllib/correlations_example.py %}
 </div>
 
 </div>
 
 ## Stratified sampling
 
 Unlike the other statistics functions, which reside in `spark.mllib`, stratified sampling methods,
 `sampleByKey` and `sampleByKeyExact`, can be performed on RDD's of key-value pairs. For stratified
 sampling, the keys can be thought of as a label and the value as a specific attribute. For example
 the key can be man or woman, or document ids, and the respective values can be the list of ages
 of the people in the population or the list of words in the documents. The `sampleByKey` method
 will flip a coin to decide whether an observation will be sampled or not, therefore requires one
 pass over the data, and provides an *expected* sample size. `sampleByKeyExact` requires significant
 more resources than the per-stratum simple random sampling used in `sampleByKey`, but will provide
 the exact sampling size with 99.99% confidence. `sampleByKeyExact` is currently not supported in
 python.
 
 <div class="codetabs">
 <div data-lang="scala" markdown="1">
 [`sampleByKeyExact()`](api/scala/org/apache/spark/rdd/PairRDDFunctions.html) allows users to
 sample exactly $\lceil f_k \cdot n_k \rceil \, \forall k \in K$ items, where $f_k$ is the desired
 fraction for key $k$, $n_k$ is the number of key-value pairs for key $k$, and $K$ is the set of
 keys. Sampling without replacement requires one additional pass over the RDD to guarantee sample
 size, whereas sampling with replacement requires two additional passes.
 
 {% include_example scala/org/apache/spark/examples/mllib/StratifiedSamplingExample.scala %}
 </div>
 
 <div data-lang="java" markdown="1">
 [`sampleByKeyExact()`](api/java/org/apache/spark/api/java/JavaPairRDD.html) allows users to
 sample exactly $\lceil f_k \cdot n_k \rceil \, \forall k \in K$ items, where $f_k$ is the desired
 fraction for key $k$, $n_k$ is the number of key-value pairs for key $k$, and $K$ is the set of
 keys. Sampling without replacement requires one additional pass over the RDD to guarantee sample
 size, whereas sampling with replacement requires two additional passes.
 
 {% include_example java/org/apache/spark/examples/mllib/JavaStratifiedSamplingExample.java %}
 </div>
 <div data-lang="python" markdown="1">
 [`sampleByKey()`](api/python/pyspark.html#pyspark.RDD.sampleByKey) allows users to
 sample approximately $\lceil f_k \cdot n_k \rceil \, \forall k \in K$ items, where $f_k$ is the
 desired fraction for key $k$, $n_k$ is the number of key-value pairs for key $k$, and $K$ is the
 set of keys.
 
 *Note:* `sampleByKeyExact()` is currently not supported in Python.
 
 {% include_example python/mllib/stratified_sampling_example.py %}
 </div>
 
 </div>
 
 ## Hypothesis testing
 
 Hypothesis testing is a powerful tool in statistics to determine whether a result is statistically
 significant, whether this result occurred by chance or not. `spark.mllib` currently supports Pearson's
 chi-squared ( $\chi^2$) tests for goodness of fit and independence. The input data types determine
 whether the goodness of fit or the independence test is conducted. The goodness of fit test requires
 an input type of `Vector`, whereas the independence test requires a `Matrix` as input.
 
 `spark.mllib` also supports the input type `RDD[LabeledPoint]` to enable feature selection via chi-squared
 independence tests.
 
 <div class="codetabs">
 <div data-lang="scala" markdown="1">
 [`Statistics`](api/scala/org/apache/spark/mllib/stat/Statistics$.html) provides methods to
 run Pearson's chi-squared tests. The following example demonstrates how to run and interpret
 hypothesis tests.
 
 {% include_example scala/org/apache/spark/examples/mllib/HypothesisTestingExample.scala %}
 </div>
 
 <div data-lang="java" markdown="1">
 [`Statistics`](api/java/org/apache/spark/mllib/stat/Statistics.html) provides methods to
 run Pearson's chi-squared tests. The following example demonstrates how to run and interpret
 hypothesis tests.
 
 Refer to the [`ChiSqTestResult` Java docs](api/java/org/apache/spark/mllib/stat/test/ChiSqTestResult.html) for details on the API.
 
 {% include_example java/org/apache/spark/examples/mllib/JavaHypothesisTestingExample.java %}
 </div>
 
 <div data-lang="python" markdown="1">
 [`Statistics`](api/python/index.html#pyspark.mllib.stat.Statistics$) provides methods to
 run Pearson's chi-squared tests. The following example demonstrates how to run and interpret
 hypothesis tests.
 
 Refer to the [`Statistics` Python docs](api/python/pyspark.mllib.html#pyspark.mllib.stat.Statistics) for more details on the API.
 
 {% include_example python/mllib/hypothesis_testing_example.py %}
 </div>
 
 </div>
 
 Additionally, `spark.mllib` provides a 1-sample, 2-sided implementation of the Kolmogorov-Smirnov (KS) test
 for equality of probability distributions. By providing the name of a theoretical distribution
 (currently solely supported for the normal distribution) and its parameters, or a function to
 calculate the cumulative distribution according to a given theoretical distribution, the user can
 test the null hypothesis that their sample is drawn from that distribution. In the case that the
 user tests against the normal distribution (`distName="norm"`), but does not provide distribution
 parameters, the test initializes to the standard normal distribution and logs an appropriate
 message.
 
 <div class="codetabs">
 <div data-lang="scala" markdown="1">
 [`Statistics`](api/scala/org/apache/spark/mllib/stat/Statistics$.html) provides methods to
 run a 1-sample, 2-sided Kolmogorov-Smirnov test. The following example demonstrates how to run
 and interpret the hypothesis tests.
 
 Refer to the [`Statistics` Scala docs](api/scala/org/apache/spark/mllib/stat/Statistics$.html) for details on the API.
 
 {% include_example scala/org/apache/spark/examples/mllib/HypothesisTestingKolmogorovSmirnovTestExample.scala %}
 </div>
 
 <div data-lang="java" markdown="1">
 [`Statistics`](api/java/org/apache/spark/mllib/stat/Statistics.html) provides methods to
 run a 1-sample, 2-sided Kolmogorov-Smirnov test. The following example demonstrates how to run
 and interpret the hypothesis tests.
 
 Refer to the [`Statistics` Java docs](api/java/org/apache/spark/mllib/stat/Statistics.html) for details on the API.
 
 {% include_example java/org/apache/spark/examples/mllib/JavaHypothesisTestingKolmogorovSmirnovTestExample.java %}
 </div>
 
 <div data-lang="python" markdown="1">
 [`Statistics`](api/python/pyspark.mllib.html#pyspark.mllib.stat.Statistics) provides methods to
 run a 1-sample, 2-sided Kolmogorov-Smirnov test. The following example demonstrates how to run
 and interpret the hypothesis tests.
 
 Refer to the [`Statistics` Python docs](api/python/pyspark.mllib.html#pyspark.mllib.stat.Statistics) for more details on the API.
 
 {% include_example python/mllib/hypothesis_testing_kolmogorov_smirnov_test_example.py %}
 </div>
 </div>
 
 ### Streaming Significance Testing
 `spark.mllib` provides online implementations of some tests to support use cases
 like A/B testing. These tests may be performed on a Spark Streaming
 `DStream[(Boolean, Double)]` where the first element of each tuple
 indicates control group (`false`) or treatment group (`true`) and the
 second element is the value of an observation.
 
 Streaming significance testing supports the following parameters:
 
 * `peacePeriod` - The number of initial data points from the stream to
 ignore, used to mitigate novelty effects.
 * `windowSize` - The number of past batches to perform hypothesis
 testing over. Setting to `0` will perform cumulative processing using
 all prior batches.
 
 
 <div class="codetabs">
 <div data-lang="scala" markdown="1">
 [`StreamingTest`](api/scala/org/apache/spark/mllib/stat/test/StreamingTest.html)
 provides streaming hypothesis testing.
 
 {% include_example scala/org/apache/spark/examples/mllib/StreamingTestExample.scala %}
 </div>
 
 <div data-lang="java" markdown="1">
 [`StreamingTest`](api/java/index.html#org.apache.spark.mllib.stat.test.StreamingTest)
 provides streaming hypothesis testing.
 
 {% include_example java/org/apache/spark/examples/mllib/JavaStreamingTestExample.java %}
 </div>
 </div>
 
 
 ## Random data generation
 
 Random data generation is useful for randomized algorithms, prototyping, and performance testing.
 `spark.mllib` supports generating random RDDs with i.i.d. values drawn from a given distribution:
 uniform, standard normal, or Poisson.
 
 <div class="codetabs">
 <div data-lang="scala" markdown="1">
 [`RandomRDDs`](api/scala/org/apache/spark/mllib/random/RandomRDDs$.html) provides factory
 methods to generate random double RDDs or vector RDDs.
 The following example generates a random double RDD, whose values follows the standard normal
 distribution `N(0, 1)`, and then map it to `N(1, 4)`.
 
 Refer to the [`RandomRDDs` Scala docs](api/scala/org/apache/spark/mllib/random/RandomRDDs$.html) for details on the API.
 
 {% highlight scala %}
 import org.apache.spark.SparkContext
 import org.apache.spark.mllib.random.RandomRDDs._
 
 val sc: SparkContext = ...
 
 // Generate a random double RDD that contains 1 million i.i.d. values drawn from the
 // standard normal distribution `N(0, 1)`, evenly distributed in 10 partitions.
 val u = normalRDD(sc, 1000000L, 10)
 // Apply a transform to get a random double RDD following `N(1, 4)`.
 val v = u.map(x => 1.0 + 2.0 * x)
 {% endhighlight %}
 </div>
 
 <div data-lang="java" markdown="1">
 [`RandomRDDs`](api/java/index.html#org.apache.spark.mllib.random.RandomRDDs) provides factory
 methods to generate random double RDDs or vector RDDs.
 The following example generates a random double RDD, whose values follows the standard normal
 distribution `N(0, 1)`, and then map it to `N(1, 4)`.
 
 Refer to the [`RandomRDDs` Java docs](api/java/org/apache/spark/mllib/random/RandomRDDs) for details on the API.
 
 {% highlight java %}
 import org.apache.spark.SparkContext;
 import org.apache.spark.api.JavaDoubleRDD;
 import static org.apache.spark.mllib.random.RandomRDDs.*;
 
 JavaSparkContext jsc = ...
 
 // Generate a random double RDD that contains 1 million i.i.d. values drawn from the
 // standard normal distribution `N(0, 1)`, evenly distributed in 10 partitions.
 JavaDoubleRDD u = normalJavaRDD(jsc, 1000000L, 10);
 // Apply a transform to get a random double RDD following `N(1, 4)`.
 JavaDoubleRDD v = u.mapToDouble(x -> 1.0 + 2.0 * x);
 {% endhighlight %}
 </div>
 
 <div data-lang="python" markdown="1">
 [`RandomRDDs`](api/python/pyspark.mllib.html#pyspark.mllib.random.RandomRDDs) provides factory
 methods to generate random double RDDs or vector RDDs.
 The following example generates a random double RDD, whose values follows the standard normal
 distribution `N(0, 1)`, and then map it to `N(1, 4)`.
 
 Refer to the [`RandomRDDs` Python docs](api/python/pyspark.mllib.html#pyspark.mllib.random.RandomRDDs) for more details on the API.
 
 {% highlight python %}
 from pyspark.mllib.random import RandomRDDs
 
 sc = ... # SparkContext
 
 # Generate a random double RDD that contains 1 million i.i.d. values drawn from the
 # standard normal distribution `N(0, 1)`, evenly distributed in 10 partitions.
 u = RandomRDDs.normalRDD(sc, 1000000L, 10)
 # Apply a transform to get a random double RDD following `N(1, 4)`.
 v = u.map(lambda x: 1.0 + 2.0 * x)
 {% endhighlight %}
 </div>
 </div>
 
 ## Kernel density estimation
 
 [Kernel density estimation](https://en.wikipedia.org/wiki/Kernel_density_estimation) is a technique
 useful for visualizing empirical probability distributions without requiring assumptions about the
 particular distribution that the observed samples are drawn from. It computes an estimate of the
 probability density function of a random variables, evaluated at a given set of points. It achieves
 this estimate by expressing the PDF of the empirical distribution at a particular point as the
 mean of PDFs of normal distributions centered around each of the samples.
 
 <div class="codetabs">
 
 <div data-lang="scala" markdown="1">
 [`KernelDensity`](api/scala/org/apache/spark/mllib/stat/KernelDensity.html) provides methods
 to compute kernel density estimates from an RDD of samples. The following example demonstrates how
 to do so.
 
 Refer to the [`KernelDensity` Scala docs](api/scala/org/apache/spark/mllib/stat/KernelDensity.html) for details on the API.
 
 {% include_example scala/org/apache/spark/examples/mllib/KernelDensityEstimationExample.scala %}
 </div>
 
 <div data-lang="java" markdown="1">
 [`KernelDensity`](api/java/index.html#org.apache.spark.mllib.stat.KernelDensity) provides methods
 to compute kernel density estimates from an RDD of samples. The following example demonstrates how
 to do so.
 
 Refer to the [`KernelDensity` Java docs](api/java/org/apache/spark/mllib/stat/KernelDensity.html) for details on the API.
 
 {% include_example java/org/apache/spark/examples/mllib/JavaKernelDensityEstimationExample.java %}
 </div>
 
 <div data-lang="python" markdown="1">
 [`KernelDensity`](api/python/pyspark.mllib.html#pyspark.mllib.stat.KernelDensity) provides methods
 to compute kernel density estimates from an RDD of samples. The following example demonstrates how
 to do so.
 
 Refer to the [`KernelDensity` Python docs](api/python/pyspark.mllib.html#pyspark.mllib.stat.KernelDensity) for more details on the API.
 
 {% include_example python/mllib/kernel_density_estimation_example.py %}
 </div>
 
 </div>

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