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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67
67
5.4 対数正規分布
図
5-6
出生時体重の正規確率プロット
5.4
対数正規分布
値集合の対数が正規分布に従うとき、その値は対数正規分布（
lognormal
distribution
）を持つと言います。対数正規分布の
CDF
は正規分布の
CDF
の
x
を
log x
に置き換えたものと同じになります。
CDF
lognormal
(x)
＝
CDF
normal
(log x)
対数正規分布はμとσの
2
つの母数で表されますが、これらは平均と標準偏差を表
すものではないことに注意してください。対数正規分布の平均は
exp(
μ＋σ
2
/2)
と
なり、標準偏差はもっとややこしい形になります（
Wikipedia
の対数正規分布の項目
参照）
†
。
標本がほぼ対数正規分布なら、その
CDF
を
log-x
軸上にプロットすれば、正規分
布の特徴的な形になります。標本が対数正規モデルにどの程度よく適合しているかを
見るためには、標本の値の対数を使って正規確率プロットをすればいいのです。
†
訳注：原文、英語は、
http://en.wikipedia.org/wiki/Log-normal_distribution
。日本語より若干詳しい、
どちらも分散の式は載っているが、標準偏差の式は実は載っていない。でも分散から簡単に計算できるだ
ろう。
正規確率プロット
全新生児
満期出産
平均値からの標準偏差
68
5 章 分布をモデル化する
例として、対数正規で近似できる成人体重の分布を見てみましょう
†
。
米国慢性病予防・健康増進センターは行動危険因子サーベイランスシステム ...
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I wanted to learn C and C++, but it didn't click for me until I picked up an O'Reilly book. When I went on the O’Reilly platform, I was astonished to find all the books there, plus live events and sandboxes so you could play around with the technology.Addison B.
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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.