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

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。

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。

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。

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)

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)

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)

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)

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)

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)

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)

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)

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)

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)

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)

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)

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)

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)
NA
rnorm(K)
rnorm(K)
NArnorm(K)
NArnorm(K)
NArnorm(K)
NArnorm(K)
NArnorm(K)

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)

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)

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)

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)

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)

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)
NA
rnorm(K)
rnorm(K)
NArnorm(K)
NArnorm(K)
NArnorm(K)
NArnorm(K)
NArnorm(K)

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)

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)
NA
rnorm(K)
rnorm(K)
NArnorm(K)
NArnorm(K)
NArnorm(K)
NArnorm(K)
NArnorm(K)

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)

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)
NA
rnorm(K)
rnorm(K)
NArnorm(K)
NArnorm(K)
NArnorm(K)
NArnorm(K)
NArnorm(K)

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)
NA
rnorm(K)
rnorm(K)
NArnorm(K)
NArnorm(K)
NArnorm(K)
NArnorm(K)
NArnorm(K)

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)

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)

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)
NA
rnorm(K)
rnorm(K)
NArnorm(K)
NArnorm(K)
NArnorm(K)
NArnorm(K)
NArnorm(K)

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)

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)

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)

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)

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))
}

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

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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