August 2015
Intermediate to advanced
272 pages
5h 46m
Japanese
Content preview from Think Stats 第2版 ―プログラマのための統計入門
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69
69
5.5 パレート分布
図
5-8
は成人体重
w
とその対数
log
10
w
との正規確率プロットを示します。データ
が正規モデルからずれていることは明らかです。対数正規モデルは、平均値から
2
、
3
標準偏差の範囲内ではよく適合していますが、裾では多少ずれています。このデー
タには、対数正規分布が良いモデルだと結論付けられます。
図
5-8
線形尺度（左）と対数尺度（右）での成人体重の正規確率プロット
5.5
パレート分布
パレート分布（
Pareto distribution
）は経済学者のヴィルフレド・パレート（
Vilfredo
Pareto
）の名に因んで名付けられています。彼はこの分布を用いて富の偏在（詳細は
Wikipedia
の「パレート分布」を参照してください
†
）を明らかにしました。それ以来、
この分布は自然や社会科学におけるさまざまな現象、例えば、都市や町、砂粒や隕石、
森林火災や地震の大きさなどを記述するのに用いられてきました。
パレート分布の
CDF
は次のようになります。
CDF(x)
＝
1
−
(
x
−
x
m
)
−
α
ここで、母数
x
m
と
α
は分布の位置と形状を規定します。
x
m
は、取り得る最小の
値です。図
5-9
は、
x
m
＝
0.5
のときの
α
のさまざまな値に対するパレート分布の
CDF
を示します。
†
訳注：英文では、
http://en.wikipedia.org/wiki/Pareto_distribution
。日本語よりも詳しい。
体重（kg）
モデル
体重
体重（log10 kg）
モデル
体重
70
5 章 分布をモデル化する
図
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I'm always learning. So when I got on to O'Reilly, I was like a kid in a candy store. There are playlists. There are answers. There's on-demand training. It's worth its weight in gold, in terms of what it allows me to do.