More efficient distribution sampling.

See peelframework/peel#82.

flink-hashagg-datagens/src/main/scala/de/tu_berlin/dima/experiments/flink/hashagg/datagen/flink/Distributions.scala

@@ -1,6 +1,6 @@
 package de.tu_berlin.dima.experiments.flink.hashagg.datagen.flink
 
-import org.apache.commons.math3.distribution.{ZipfDistribution, BinomialDistribution, UniformIntegerDistribution}
+import org.apache.commons.math3.distribution._
 
 object Distributions {
 
@@ -13,13 +13,21 @@ object Distributions {
     def sample(cp: Double) = distribution.inverseCumulativeProbability(cp)
   }
 
-  case class Binomial(sampleSize: Int, successProbability: Double) extends DiscreteDistribution {
-    val distribution = new BinomialDistribution(sampleSize - 1, successProbability)
-    def sample(cp: Double) = distribution.inverseCumulativeProbability(cp) - 1
+  // approximated by NormalDistribution, since BinomialDistribution is too slow
+  // for the relationship between the two, see this article
+  // http://www.real-statistics.com/binomial-and-related-distributions/relationship-binomial-and-normal-distributions/
+  case class Binomial(sampleSize: Int, p: Double) extends DiscreteDistribution {
+    val n = sampleSize - 1
+    val distribution = new NormalDistribution(n * p, Math.sqrt(n * p * (1 - p)))
+    def sample(cp: Double) = (distribution.inverseCumulativeProbability(cp) - 1).toInt % n
   }
 
+  // TODO: since BinomialDistribution is too slow, either approximate with ParetoDistribution or write custom CDF^{-1}
+  // for the relationship between the two, see this article
+  // http://www.hpl.hp.com/research/idl/papers/ranking/ranking.html
   case class Zipf(sampleSize: Int, exponent: Double) extends DiscreteDistribution {
-    val distribution = new ZipfDistribution(sampleSize, exponent)
-    def sample(cp: Double) = distribution.inverseCumulativeProbability(cp) - 1
+    val n = sampleSize
+    val distribution = new ParetoDistribution(1, 1 + 1/exponent)
+    def sample(cp: Double) = (distribution.inverseCumulativeProbability(cp) - 1).toInt % n
   }
 }