Github user feynmanliang commented on a diff in the pull request:
https://github.com/apache/spark/pull/7278#discussion_r34304312
--- Diff:
mllib/src/main/scala/org/apache/spark/mllib/stat/test/ADTest.scala ---
@@ -0,0 +1,264 @@
+/*
+ * 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.mllib.stat.test
+
+import collection.immutable.ListMap
+
+import org.apache.commons.math3.distribution.{ExponentialDistribution,
GumbelDistribution,
+ LogisticDistribution, NormalDistribution, WeibullDistribution}
+
+import org.apache.spark.rdd.RDD
+
+/**
+ * The Anderson Darling (AD) test, similarly to the Kolmogorov Smirnov
(KS) test, tests whether the
+ * data follow a given theoretical distribution. It should be used with
continuous data and
+ * assumes that no ties occur (the presence of ties can affect the
validity of the test).
+ * The AD test provides an alternative to the Kolmogorov-Smirnov test.
Namely, it is better
+ * suited to identify departures from the theoretical distribution at the
tails.
+ * It is worth noting that the the AD test's critical values depend on the
+ * distribution being tested against.
+ * The AD statistic is defined as -n - s/n, where
+ * s = sum from i=1 to n of (2i + 1)(ln(z_i) + ln(1 - z_{n+1-i})
+ * where z_i is the CDF value of the ith observation in the sorted sample.
+ * For more information
@see[[https://en.wikipedia.org/wiki/Anderson%E2%80%93Darling_test]]
+ */
+private[stat] object ADTest {
+
+ object NullHypothesis extends Enumeration {
+ type NullHypothesis = Value
+ val oneSample = Value("Sample follows theoretical distribution.")
+ }
+
+ /**
+ * ADTheoreticalDist is a trait that every distribution used in an AD
test must extend.
+ * The rationale for this is that the AD test has distribution-dependent
critical values, and by
+ * requiring extension of this trait we guarantee that future additional
distributions
+ * make sure to add the appropriate critical values (CVs) (or at least
acknowledge
+ * that they should be added)
+ */
+ sealed trait ADTheoreticalDist {
+ val params: Array[Double] // parameters used to initialized the
distribution
+
+ def cdf(x: Double): Double // calculate the cdf under the given
distribution for value x
+
+ def getCVs(n: Double): Map[Double, Double] // return appropriate CVs,
adjusted for sample size
+ }
+
+ /**
+ * Sourced from
+ *
http://civil.colorado.edu/~balajir/CVEN5454/lectures/Ang-n-Tang-Chap7-Goodness-of-fit-PDFs-
+ * test.pdf
+ *
https://github.com/scipy/scipy/blob/v0.15.1/scipy/stats/morestats.py#L1017
+ */
+
+ // Exponential distribution
+ class ADExponential(val params: Array[Double]) extends ADTheoreticalDist
{
+ private val theoretical = new ExponentialDistribution(params(0))
+
+ private val rawCVs = ListMap(
+ 0.15 -> 0.922, 0.10 -> 1.078,
+ 0.05 -> 1.341, 0.025 -> 1.606, 0.01 -> 1.957
+ )
+
+ def cdf(x: Double): Double = theoretical.cumulativeProbability(x)
+
+ def getCVs(n: Double): Map[Double, Double] = {
+ rawCVs.map { case (sig, cv) => sig -> cv / (1 + 0.6 / n)}
+ }
+ }
+
+ // Normal Distribution
+ class ADNormal(val params: Array[Double]) extends ADTheoreticalDist {
+ private val theoretical = new NormalDistribution(params(0), params(1))
+
+ private val rawCVs = ListMap(
+ 0.15 -> 0.576, 0.10 -> 0.656,
+ 0.05 -> 0.787, 0.025 -> 0.918, 0.01 -> 1.092
+ )
+
+ def cdf(x: Double): Double = theoretical.cumulativeProbability(x)
+
+ def getCVs(n: Double): Map[Double, Double] = {
+ rawCVs.map { case (sig, cv) => sig -> cv / (1 + 4.0 / n - 25.0 / (n
* n)) }
+ }
+ }
+
+ // Gumbel distribution
+ class ADGumbel(val params: Array[Double]) extends ADTheoreticalDist {
+ private val theoretical = new GumbelDistribution(params(0), params(1))
+
+ private val rawCVs = ListMap(
+ 0.25 -> 0.474, 0.10 -> 0.637,
+ 0.05 -> 0.757, 0.025 -> 0.877, 0.01 -> 1.038
+ )
+
+ def cdf(x: Double): Double = theoretical.cumulativeProbability(x)
+
+ def getCVs(n: Double): Map[Double, Double] = {
+ rawCVs.map { case (sig, cv) => sig -> cv / (1 + 0.2 / math.sqrt(n))}
+ }
+ }
+
+ // Logistic distribution
+ class ADLogistic(val params: Array[Double]) extends ADTheoreticalDist {
+ private val theoretical = new LogisticDistribution(params(0),
params(1))
+
+ private val rawCVs = ListMap(
+ 0.25 -> 0.426, 0.10 -> 0.563, 0.05 -> 0.660,
+ 0.025 -> 0.769, 0.01 -> 0.906, 0.005 -> 1.010
+ )
+
+ def cdf(x: Double): Double = theoretical.cumulativeProbability(x)
+
+ def getCVs(n: Double): Map[Double, Double] = {
+ rawCVs.map { case (sig, cv) => sig -> cv / (1 + 0.25 / n)}
+ }
+ }
+
+ // Weibull distribution
+ class ADWeibull(val params: Array[Double]) extends ADTheoreticalDist {
+ private val theoretical = new WeibullDistribution(params(0), params(1))
+
+ private val rawCVs = ListMap(
+ 0.25 -> 0.474, 0.10 -> 0.637,
+ 0.05 -> 0.757, 0.025 -> 0.877, 0.01 -> 1.038
+ )
+
+ def cdf(x: Double): Double = theoretical.cumulativeProbability(x)
+
+ def getCVs(n: Double): Map[Double, Double] = {
+ rawCVs.map { case (sig, cv) => sig -> cv / (1 + 0.2 / math.sqrt(n))}
+ }
+ }
+
+ /**
+ * Perform a one sample Anderson Darling test
+ * @param data `RDD[Double]` data to test for a given distribution
--- End diff --
Types are unnecessary here, ditto for the other scaladocs
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