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@ynakayama

# 連続型確率分布

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# 連続型の確率分布

## 連続一様分布

U(a,b)


U(0,1) に従う一様乱数から所与の確率分布に従う乱数を発生させることができます。

## 正規分布 (ガウス分布)

f(x) = \frac 1 {\sqrt{2\pi\sigma}} exp \{-(x-\mu)^2/2{\sigma^2}\} \\
(-\infty \lt x \lt \infty)


## 指数分布

これも以前書きましたが再掲。

f(x) = {\lambda}e^{-{\lambda}x} \\
(x\ge0), 0 (x\lt0)


## ガンマ分布

\frac {\beta^{\alpha}} {\Gamma(\alpha)}x^{\alpha - 1}exp(-{\beta}x) \\
(x \gt 0)


## ベータ分布

\frac 1 {B(\alpha, \beta)} x^{\alpha-1}(1-x)^{\beta-1} \\
(0 \lt x \lt 1)


## コーシー分布

f(x) = \frac 1 x \frac 1 {x^2 + 1}


## 対数正規分布

log X が正規分布 N(μ, σ^2) に従う分布。

## ワイブル分布

cx^bexp(-\frac {cx^{b+1}} {b+1}) \\
(x \gt 0)


## ロジスティック分布

F(x) = \frac 1 {1 + exp(-x)}


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