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Change-Id: I52a325624a7f0dd652b362a9840626d6d9f3c42b

1 files changed, 144 insertions, 0 deletions

diff --git a/src/main/java/org/apache/commons/math/stat/inference/UnknownDistributionChiSquareTest.java b/src/main/java/org/apache/commons/math/stat/inference/UnknownDistributionChiSquareTest.java
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+/*
+ * 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.commons.math.stat.inference;
+
+import org.apache.commons.math.MathException;
+
+/**
+ * An interface for Chi-Square tests for unknown distributions.
+ * <p>Two samples tests are used when the distribution is unknown <i>a priori</i>
+ * but provided by one sample. We compare the second sample against the first.</p>
+ *
+ * @version $Revision: 811685 $ $Date: 2009-09-05 19:36:48 +0200 (sam. 05 sept. 2009) $
+ * @since 1.2
+ */
+public interface UnknownDistributionChiSquareTest extends ChiSquareTest {
+
+    /**
+     * <p>Computes a
+     * <a href="http://www.itl.nist.gov/div898/software/dataplot/refman1/auxillar/chi2samp.htm">
+     * Chi-Square two sample test statistic</a> comparing bin frequency counts
+     * in <code>observed1</code> and <code>observed2</code>.  The
+     * sums of frequency counts in the two samples are not required to be the
+     * same.  The formula used to compute the test statistic is</p>
+     * <code>
+     * &sum;[(K * observed1[i] - observed2[i]/K)<sup>2</sup> / (observed1[i] + observed2[i])]
+     * </code> where
+     * <br/><code>K = &sqrt;[&sum(observed2 / &sum;(observed1)]</code>
+     * </p>
+     * <p>This statistic can be used to perform a Chi-Square test evaluating the null hypothesis that
+     * both observed counts follow the same distribution.</p>
+     * <p>
+     * <strong>Preconditions</strong>: <ul>
+     * <li>Observed counts must be non-negative.
+     * </li>
+     * <li>Observed counts for a specific bin must not both be zero.
+     * </li>
+     * <li>Observed counts for a specific sample must not all be 0.
+     * </li>
+     * <li>The arrays <code>observed1</code> and <code>observed2</code> must have the same length and
+     * their common length must be at least 2.
+     * </li></ul></p><p>
+     * If any of the preconditions are not met, an
+     * <code>IllegalArgumentException</code> is thrown.</p>
+     *
+     * @param observed1 array of observed frequency counts of the first data set
+     * @param observed2 array of observed frequency counts of the second data set
+     * @return chiSquare statistic
+     * @throws IllegalArgumentException if preconditions are not met
+     */
+    double chiSquareDataSetsComparison(long[] observed1, long[] observed2)
+        throws IllegalArgumentException;
+
+    /**
+     * <p>Returns the <i>observed significance level</i>, or <a href=
+     * "http://www.cas.lancs.ac.uk/glossary_v1.1/hyptest.html#pvalue">
+     * p-value</a>, associated with a Chi-Square two sample test comparing
+     * bin frequency counts in <code>observed1</code> and
+     * <code>observed2</code>.
+     * </p>
+     * <p>The number returned is the smallest significance level at which one
+     * can reject the null hypothesis that the observed counts conform to the
+     * same distribution.
+     * </p>
+     * <p>See {@link #chiSquareDataSetsComparison(long[], long[])} for details
+     * on the formula used to compute the test statistic. The degrees of
+     * of freedom used to perform the test is one less than the common length
+     * of the input observed count arrays.
+     * </p>
+     * <strong>Preconditions</strong>: <ul>
+     * <li>Observed counts must be non-negative.
+     * </li>
+     * <li>Observed counts for a specific bin must not both be zero.
+     * </li>
+     * <li>Observed counts for a specific sample must not all be 0.
+     * </li>
+     * <li>The arrays <code>observed1</code> and <code>observed2</code> must
+     * have the same length and
+     * their common length must be at least 2.
+     * </li></ul><p>
+     * If any of the preconditions are not met, an
+     * <code>IllegalArgumentException</code> is thrown.</p>
+     *
+     * @param observed1 array of observed frequency counts of the first data set
+     * @param observed2 array of observed frequency counts of the second data set
+     * @return p-value
+     * @throws IllegalArgumentException if preconditions are not met
+     * @throws MathException if an error occurs computing the p-value
+     */
+    double chiSquareTestDataSetsComparison(long[] observed1, long[] observed2)
+      throws IllegalArgumentException, MathException;
+
+    /**
+     * <p>Performs a Chi-Square two sample test comparing two binned data
+     * sets. The test evaluates the null hypothesis that the two lists of
+     * observed counts conform to the same frequency distribution, with
+     * significance level <code>alpha</code>.  Returns true iff the null
+     * hypothesis can be rejected with 100 * (1 - alpha) percent confidence.
+     * </p>
+     * <p>See {@link #chiSquareDataSetsComparison(long[], long[])} for
+     * details on the formula used to compute the Chisquare statistic used
+     * in the test. The degrees of of freedom used to perform the test is
+     * one less than the common length of the input observed count arrays.
+     * </p>
+     * <strong>Preconditions</strong>: <ul>
+     * <li>Observed counts must be non-negative.
+     * </li>
+     * <li>Observed counts for a specific bin must not both be zero.
+     * </li>
+     * <li>Observed counts for a specific sample must not all be 0.
+     * </li>
+     * <li>The arrays <code>observed1</code> and <code>observed2</code> must
+     * have the same length and their common length must be at least 2.
+     * </li>
+     * <li> <code> 0 < alpha < 0.5 </code>
+     * </li></ul><p>
+     * If any of the preconditions are not met, an
+     * <code>IllegalArgumentException</code> is thrown.</p>
+     *
+     * @param observed1 array of observed frequency counts of the first data set
+     * @param observed2 array of observed frequency counts of the second data set
+     * @param alpha significance level of the test
+     * @return true iff null hypothesis can be rejected with confidence
+     * 1 - alpha
+     * @throws IllegalArgumentException if preconditions are not met
+     * @throws MathException if an error occurs performing the test
+     */
+    boolean chiSquareTestDataSetsComparison(long[] observed1, long[] observed2, double alpha)
+      throws IllegalArgumentException, MathException;
+
+}