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ド素人の統計勉強メモ with Scala ~ ガウス分布編

Last updated at Posted at 2015-06-01

使用するライブラリ

Breeze

sbt
name := "Stats"

version := "1.0"

scalaVersion := "2.11.6"
    
libraryDependencies  ++= Seq(
  // other dependencies here
  "org.scalanlp" %% "breeze" % "0.11.2",
  // native libraries are not included by default. add this if you want them (as of 0.7)
  // native libraries greatly improve performance, but increase jar sizes.
  "org.scalanlp" %% "breeze-natives" % "0.11.2",
  "org.scalanlp" %% "breeze-viz" % "0.8"
)

resolvers ++= Seq(
  // other resolvers here
  // if you want to use snapshot builds (currently 0.12-SNAPSHOT), use this.
  "Sonatype Snapshots" at "https://oss.sonatype.org/content/repositories/snapshots/",
  "Sonatype Releases" at "https://oss.sonatype.org/content/repositories/releases/"
)

ガウス分布

Gaussianを使う。

引数はμ(ミュー)とσ(シグマ)

  • μ: 分布の平均

  • σ: 標準偏差

やってみる

Main.scala

/**
 * Created by FScoward on 15/06/01.
 */

import breeze.linalg.{sum, DenseVector}
import breeze.numerics.{sqrt, pow}
import breeze.plot.Figure
import breeze.stats.distributions.Gaussian
import breeze.plot._

object Main {
  
  def main(args: Array[String]): Unit = {
    
    // 例えば10人の生徒がテストでそれぞれ以下の点数を取ったとする。
    val dv = DenseVector(61, 74, 55, 85, 68, 72, 64, 80, 82, 59)
    
    // μ: 分布の平均
    val mu = sum(dv) / dv.length
    // σ: 標準偏差
    val sigma = sqrt(sum(dv.map(x => pow(mu - x, 2))) / dv.length)
    
    val figure = Figure()
    val gaussian = Gaussian(mu, sigma)
    // subplot(m,n,p) は、現在の Figure を m 行 n 列のグリッドに分割し、p で指定された位置のサブプロットに座標軸を作成します
    // つまりグラフをどこに配置するかという話。
    val p = figure.subplot(0)
    // 100点満点
    val maxScore = 100
    // 条件を付けてやらないと100点を突き抜ける
    p += hist(gaussian.condition(_ <= maxScore).sample(5000), maxScore, "Hist")
    p.xlabel = "点数"
    p.ylabel = "人数"
    figure.saveas("gaussian.png")
  }
}

出力(ヒストグラム)

histogram.png

参考資料

Think Stats ―プログラマのための統計入門

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