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How Random Points distributes on a plane? (To see the variety of the shape)

2次元上に点をばらまいた時の形の多様性を考察することで、何かのデータを採集した時の偏り・揺らぎが実際どの程度起こるだろうかについての理屈を考察するために、メモ的なシミュレーションを行いました。2次元の上にx座標とy座標が独立に標準正規分布となるような点を単にN個並べた単純なものですが、実際見てみると、様々な知見が得ることが出来ます。

この文書を作ろうとした直接的な動機は、全くのっぺらぼうな感じの分布である2次元正規分布から数十個の点を取ったら、見た目にいくつかのクラスタに分かれて見えることが多い、という現象をきちんと理論的に考察したい、というものです。

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How Random Points distributes on a plane? (To see the variety of the shape)

  1. 1. 同一分布N個のランダムな点の配置が 見た目に大きく異なる様子を観察するための 考察用メモ 2014-08-17 TS. 様々なNについて具体的な様子について、簡 単な知見を得たので、メモとしてここに書き残 し、後日の再検討のために参照できるように まとめたのが、この文書である。
  2. 2. 考察したかったこと(1) • 相当量のデータを集めても、データの揺らぎは 大きく見えることがある。(データを集めるにはコ ストがかかるにも関わらず!) • どの程度の揺らぎが実際に発生するか、採集す る個数Nを決め、24回ずつ、円状の2次元正規分 布からN点取り出した様子をプロットしてみた。 • 様々なNについて具体的な様子について、簡単 な知見を得たので、メモとしてここに書き残し、後 日の再検討のために参照できるようにまとめた のが、この文書である。
  3. 3. 考察したかったこと(2) • N≦15程度だと “星座” が作れる。 • N = 20 程度だと いくつかの(偽の)クラスタが作れるように見える。 • N=30だと、2変数x,yの標本平均で4分割線を引くと、4個の各象限につい て、標本の各種特徴を調べることに意味があるかもしれない。 • N=100 でも包絡線の形は多様。 • N=150 でも4分割(←x=0,y=0の2直線で切断) しても各象限について、点の 分布が同じようには一見見えない。 • N=400 位で大体まん丸くなる。 • きちんと分析目的を定めないと、どれだけの量のデータを集めたら安定 した結果が出るかについて計画が立たない、ということについての、示唆 に富んだ結果が得られたと考えられる。
  4. 4. N=5
  5. 5. N=6 NArnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NArnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NArnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NArnorm(K) NArnorm(K) NArnorm(K) NArnorm(K) NArnorm(K)
  6. 6. N=7 NArnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NArnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NArnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NArnorm(K) NArnorm(K) NArnorm(K) NArnorm(K) NArnorm(K)
  7. 7. N=8 NArnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NArnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NArnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NArnorm(K) NArnorm(K) NArnorm(K) NArnorm(K) NArnorm(K)
  8. 8. N=9 NArnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NArnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NArnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NArnorm(K) NArnorm(K) NArnorm(K) NArnorm(K) NArnorm(K)
  9. 9. N=10 NArnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NArnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NArnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NANA rnorm(K)rnorm(K) NA NA rnorm(K) rnorm(K) NArnorm(K) NArnorm(K) NArnorm(K) NArnorm(K) NArnorm(K)
  10. 10. N=12 NArnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NArnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NArnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NArnorm(K) NArnorm(K) NArnorm(K) NArnorm(K) NArnorm(K)
  11. 11. N=15 NArnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NArnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NArnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NArnorm(K) NArnorm(K) NArnorm(K) NArnorm(K) NArnorm(K)
  12. 12. N=16 NArnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NArnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NArnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NArnorm(K) NArnorm(K) NArnorm(K) NArnorm(K) NArnorm(K)
  13. 13. N=18 NArnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NArnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NArnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NArnorm(K) NArnorm(K) NArnorm(K) NArnorm(K) NArnorm(K)
  14. 14. N=20 NArnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NArnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NArnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NArnorm(K) NArnorm(K) NArnorm(K) NArnorm(K) NArnorm(K)
  15. 15. N=24 NArnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NArnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NArnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NArnorm(K) NArnorm(K) NArnorm(K) NArnorm(K) NArnorm(K)
  16. 16. N=25 NArnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NArnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NArnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NArnorm(K) NArnorm(K) NArnorm(K) NArnorm(K) NArnorm(K)
  17. 17. N=27 NArnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NArnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NArnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NArnorm(K) NArnorm(K) NArnorm(K) NArnorm(K) NArnorm(K)
  18. 18. N=30 NArnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NArnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NArnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NANA rnorm(K)rnorm(K) NA NA rnorm(K) rnorm(K) NArnorm(K) NArnorm(K) NArnorm(K) NArnorm(K) NArnorm(K)
  19. 19. N=35 NArnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NArnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NArnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NArnorm(K) NArnorm(K) NArnorm(K) NArnorm(K) NArnorm(K)
  20. 20. N=35 NArnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NArnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NArnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NArnorm(K) NArnorm(K) NArnorm(K) NArnorm(K) NArnorm(K)
  21. 21. N=40 NArnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NArnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NArnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NArnorm(K) NArnorm(K) NArnorm(K) NArnorm(K) NArnorm(K)
  22. 22. N=45 NArnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NArnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NArnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NArnorm(K) NArnorm(K) NArnorm(K) NArnorm(K) NArnorm(K)
  23. 23. N=50 NArnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NArnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NArnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NArnorm(K) NArnorm(K) NArnorm(K) NArnorm(K) NArnorm(K)
  24. 24. N=55 NArnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NArnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NArnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NArnorm(K) NArnorm(K) NArnorm(K) NArnorm(K) NArnorm(K)
  25. 25. N=60 NArnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NArnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NArnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NANA rnorm(K)rnorm(K) NA NA rnorm(K) rnorm(K) NArnorm(K) NArnorm(K) NArnorm(K) NArnorm(K) NArnorm(K)
  26. 26. N=65 NArnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NArnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NArnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NArnorm(K) NArnorm(K) NArnorm(K) NArnorm(K) NArnorm(K)
  27. 27. N=70 NArnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NArnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NArnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NANA rnorm(K)rnorm(K) NA NA rnorm(K) rnorm(K) NArnorm(K) NArnorm(K) NArnorm(K) NArnorm(K) NArnorm(K)
  28. 28. N=80 NArnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NArnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NArnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NArnorm(K) NArnorm(K) NArnorm(K) NArnorm(K) NArnorm(K)
  29. 29. N=90 NArnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NArnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NArnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NANA rnorm(K)rnorm(K) NA NA rnorm(K) rnorm(K) NArnorm(K) NArnorm(K) NArnorm(K) NArnorm(K) NArnorm(K)
  30. 30. N=100 NArnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NArnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NArnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NANA rnorm(K)rnorm(K) NA NA rnorm(K) rnorm(K) NArnorm(K) NArnorm(K) NArnorm(K) NArnorm(K) NArnorm(K)
  31. 31. N=120 NArnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NArnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NArnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NArnorm(K) NArnorm(K) NArnorm(K) NArnorm(K) NArnorm(K)
  32. 32. N=140 NArnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NArnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NArnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NArnorm(K) NArnorm(K) NArnorm(K) NArnorm(K) NArnorm(K)
  33. 33. N=150 NArnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NArnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NArnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NANA rnorm(K)rnorm(K) NA NA rnorm(K) rnorm(K) NArnorm(K) NArnorm(K) NArnorm(K) NArnorm(K) NArnorm(K)
  34. 34. N=160 NArnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NArnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NArnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NArnorm(K) NArnorm(K) NArnorm(K) NArnorm(K) NArnorm(K)
  35. 35. N=200 NArnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NArnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NArnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NArnorm(K) NArnorm(K) NArnorm(K) NArnorm(K) NArnorm(K)
  36. 36. N=400 NArnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NArnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NArnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NArnorm(K) NArnorm(K) NArnorm(K) NArnorm(K) NArnorm(K)
  37. 37. N=800 NArnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NArnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NArnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NA NA rnorm(K) rnorm(K) NArnorm(K) NArnorm(K) NArnorm(K) NArnorm(K) NArnorm(K)
  38. 38. 用いたR言語のスクリプト par(mfrow=c(4,6)) K=800;H=4; # Change the value of K to 5, 7, 10, 15, 20, 25, mar=0.2;cex=.5 # if K < 400 , set cex=1. if K >= 400 set cex=0.5 for(i in 1:24){ par(mar=rep(mar,4),xaxt="n",yaxt="n",xlab="",ylab="") plot(NA,NA,xlim=c(-H,H),ylim=c(-H,H)) ; points(0,0,pch=3,cex=15,col="gray80") par(new=T) plot(rnorm(K),rnorm(K),xlim=c(-H,H),ylim=c(-H,H) , pch=16,cex=cex) #, next par(new=T); symbols(rep(0,2),rep(0,2),circles=rep(2,2), xaxt="n", yaxt="n",xlab="",ylab="",fg="gray60",cex=3, inches=F ,xlim=c(-H,H),ylim=c(-H,H)) }
  39. 39. 正方形内一様分布(N=5,10,20,30,40,60,80,100) NArp(K) 5 NA NA rp(K) rp(K) 5 NA NA rp(K) rp(K) 5 NA NA rp(K) rp(K) 5 NA NA rp(K) rp(K) 5 NA NA rp(K) rp(K) 5 NA NA rp(K) rp(K) 5 NA NA rp(K) rp(K) 5 NA NA rp(K) rp(K) 5 NA NA rp(K) rp(K) 5 NA NA rp(K) rp(K) 5 NA NA rp(K) rp(K) 5 NArp(K) 10 NA NA rp(K) rp(K) 10 NA NA rp(K) rp(K) 10 NA NA rp(K) rp(K) 10 NA NA rp(K) rp(K) 10 NA NA rp(K) rp(K) 10 NA NA rp(K) rp(K) 10 NA NA rp(K) rp(K) 10 NA NA rp(K) rp(K) 10 NA NA rp(K) rp(K) 10 NA NA rp(K) rp(K) 10 NA NA rp(K) rp(K) 10 NArp(K) 20 NA NA rp(K) rp(K) 20 NA NA rp(K) rp(K) 20 NA NA rp(K) rp(K) 20 NA NA rp(K) rp(K) 20 NA NA rp(K) rp(K) 20 NA NA rp(K) rp(K) 20 NA NA rp(K) rp(K) 20 NA NA rp(K) rp(K) 20 NA NA rp(K) rp(K) 20 NA NA rp(K) rp(K) 20 NA NA rp(K) rp(K) 20 NArp(K) 30 NA NA rp(K) rp(K) 30 NA NA rp(K) rp(K) 30 NA NA rp(K) rp(K) 30 NA NA rp(K) rp(K) 30 NA NA rp(K) rp(K) 30 NA NA rp(K) rp(K) 30 NA NA rp(K) rp(K) 30 NA NA rp(K) rp(K) 30 NA NA rp(K) rp(K) 30 NA NA rp(K) rp(K) 30 NA NA rp(K) rp(K) 30 NArp(K) 40 NA NA rp(K) rp(K) 40 NA NA rp(K) rp(K) 40 NA NA rp(K) rp(K) 40 NA NA rp(K) rp(K) 40 NA NA rp(K) rp(K) 40 NA NA rp(K) rp(K) 40 NA NA rp(K) rp(K) 40 NA NA rp(K) rp(K) 40 NA NA rp(K) rp(K) 40 NA NA rp(K) rp(K) 40 NA NA rp(K) rp(K) 40 NArp(K) 60 NA NA rp(K) rp(K) 60 NA NA rp(K) rp(K) 60 NA NA rp(K) rp(K) 60 NA NA rp(K) rp(K) 60 NA NA rp(K) rp(K) 60 NA NA rp(K) rp(K) 60 NA NA rp(K) rp(K) 60 NA NA rp(K) rp(K) 60 NA NA rp(K) rp(K) 60 NA NA rp(K) rp(K) 60 NA NA rp(K) rp(K) 60 NArp(K) 80 NA NA rp(K) rp(K) 80 NA NA rp(K) rp(K) 80 NA NA rp(K) rp(K) 80 NA NA rp(K) rp(K) 80 NA NA rp(K) rp(K) 80 NA NA rp(K) rp(K) 80 NA NA rp(K) rp(K) 80 NA NA rp(K) rp(K) 80 NANA rp(K)rp(K) 80 NA NA rp(K) rp(K) 80 NA NA rp(K) rp(K) 80 100 NArp(K) 100 NArp(K) 100 NArp(K) 100 NArp(K) 100 NArp(K) 100 NArp(K) 100 NArp(K) 100 NArp(K) 100 NArp(K) 100 NArp(K) 100 NArp(K) 100
  40. 40. 用いたR言語のスクリプト (正方形内の一様分布) par(mfrow=c(8,12)) for(K in c(5,10,20,30,40,60,80,100)){ #K=10; H=4; # Change the value of K to 5, 7, 10, 15, 20, 25, mar=0.2;cex=sqrt(20)/sqrt(K) # if K < 400 , set cex=1. if K >= 400 set cex=0.5 rp <- function(k){runif(K,-H*.9,H*.9)} for(i in 1:12){ par(mar=rep(mar,4),xaxt="n",yaxt="n",xlab="",ylab="") plot(NA,NA,xlim=c(-H,H),ylim=c(-H,H)) ; points(0,0,pch=3,cex=15,col="gray80") par(new=T) plot(rp(K),rp(K),xlim=c(-H,H),ylim=c(-H,H) , pch=16,cex=cex) #, text(H*.93,-H*.95,paste(K),col="skyblue") next par(new=T); symbols(rep(0,2),rep(0,2),circles=rep(2,2), xaxt="n", yaxt="n",xlab="",ylab="",fg="gray60",cex=3, inches=F ,xlim=c(-H,H),ylim=c(-H,H)) } }

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