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<document>

  <properties>
    <title>Apache Commons Statistics</title>
  </properties>

  <body>

    <section name="Apache Commons Statistics" href="summary">
      <p>
        Apache Commons Statistics provides utilities for statistical applications.
      </p>


      <p>
        Descriptive statistics can be computed on array data or using the Java Stream API,
        for example:
      </p>

<source class="prettyprint">
int[] values = {1, 1, 2, 3, 5, 8, 13, 21};
double v = IntVariance.of(values).getAsDouble();   // 49.929

// A builder for specified statistics to allow
// parallel computation on a stream of values
IntStatistics.Builder builder = IntStatistics.builder(
    Statistic.MIN, Statistic.MAX, Statistic.MEAN);
IntStatistics stats =
    Stream.of("one", "two", "three", "four")
    .parallel()
    .mapToInt(String::length)
    .collect(builder::build, IntConsumer::accept, IntStatistics::combine);

stats.getAsInt(Statistic.MIN);       // 3
stats.getAsInt(Statistic.MAX);       // 5
stats.getAsDouble(Statistic.MEAN);   // 15.0 / 4
</source>

      <p>
        Support is provided for commonly used continuous and discrete distributions,
        for example:
      </p>

<source class="prettyprint">
TDistribution t = TDistribution.of(29);
double lowerTail = t.cumulativeProbability(-2.656);   // P(T(29) &lt;= -2.656)
double upperTail = t.survivalProbability(2.75);       // P(T(29) &gt; 2.75)

PoissonDistribution p = PoissonDistribution.of(4.56);
int x = p.inverseCumulativeProbability(0.99);
</source>

      <p>
        Hypothesis testing can be performed for various statistical tests, for example:
      </p>

<source class="prettyprint">
double[] math    = {53, 69, 65, 65, 67, 79, 86, 65, 62, 69};   // mean = 68.0
double[] science = {75, 65, 68, 63, 55, 65, 73, 45, 51, 52};   // mean = 61.2

SignificanceResult result = TTest.withDefaults()
                                 .with(AlternativeHypothesis.GREATER_THAN)
                                 .pairedTest(math, science);
result.getPValue();    // 0.05764
result.reject(0.05);   // false
</source>

      <p>
        For more examples and advanced usage, see the <a href="userguide/index.html">userguide</a>.
      </p>

    </section>

    <section name="Download Apache Commons Statistics">
      <subsection name="Releases">
        <p>
          Download the
          <a href="https://commons.apache.org/statistics/download_statistics.cgi">
            latest release</a> of Apache Commons Statistics.
        </p>
      </subsection>
    </section>

  </body>

</document>