[R] {stats} 確率関数まとめ

命名規則

Rの確率関数は一定の規則で命名されている。即ち関数名の１文字目(d,p,q,r)が関数の種別を表し、その後に確率分布名(xxxxx)が続く。

以下、各分布ごとに具体的な関数を列挙する。

関数名一覧

正規分布 (The Normal Distribution)

dnorm(x, mean = 0, sd = 1, log = FALSE)
pnorm(q, mean = 0, sd = 1, lower.tail = TRUE, log.p = FALSE)
qnorm(p, mean = 0, sd = 1, lower.tail = TRUE, log.p = FALSE)
rnorm(n, mean = 0, sd = 1)

# 平均ｍ、標準偏差ｎの正規分布確率密度を返す
dnorm( x, mean=m, sd=n ) #plot.it=F 密度関数グラフを描画しない
# 指定したｚ値の下側確率P(z<z値)を返す
pnorm( ｚ値 ) # lower.tail=F 指定したｚ値の上側確率P(z>z値)
# 指定した下側確率に対応するｚ値（境界値）を返す
qnorm( 確率 ) # lower.tail=F 指定した上側確率に対応するｚ値（境界値）
# 標準正規分布に従う乱数をｎ個生成する
rnorm( n ) 
# 正規分布を描画
plot( function(x) dnorm(x), from=始点, to=終点 ) # from, to省略時は-4～4の範囲を描画
# 標準正規分布を描画
curve( dnorm(x), from=始点, to=終点 ) # from～toで描画範囲を指定

一様分布 (The Uniform Distribution)

dunif(x, min = 0, max = 1, log = FALSE)
punif(q, min = 0, max = 1, lower.tail = TRUE, log.p = FALSE)
qunif(p, min = 0, max = 1, lower.tail = TRUE, log.p = FALSE)
runif(n, min = 0, max = 1)

二項分布 (The Binominal Distribution)

dbinom(x, size, prob, log = FALSE)
pbinom(q, size, prob, lower.tail = TRUE, log.p = FALSE)
qbinom(p, size, prob, lower.tail = TRUE, log.p = FALSE)
rbinom(n, size, prob)

指数分布 (The Exponential Distribution)
dexp(x, rate = 1, log = FALSE)
pexp(q, rate = 1, lower.tail = TRUE, log.p = FALSE)
qexp(p, rate = 1, lower.tail = TRUE, log.p = FALSE)
rexp(n, rate = 1)

ｔ分布 (The Student t Distribution)
dt(x, df, ncp, log = FALSE)
pt(q, df, ncp, lower.tail = TRUE, log.p = FALSE)
qt(p, df, ncp, lower.tail = TRUE, log.p = FALSE)
rt(n, df, ncp)

Ｆ分布 (The F Distribution)
df(x, df1, df2, ncp, log = FALSE)
pf(q, df1, df2, ncp, lower.tail = TRUE, log.p = FALSE)
qf(p, df1, df2, ncp, lower.tail = TRUE, log.p = FALSE)
rf(n, df1, df2, ncp)

カイ２乗分布 The (non-central) Chi-Squared Distribution

dchisq(x, df, ncp = 0, log = FALSE)
pchisq(q, df, ncp = 0, lower.tail = TRUE, log.p = FALSE)
qchisq(p, df, ncp = 0, lower.tail = TRUE, log.p = FALSE)
rchisq(n, df, ncp = 0)

ベータ分布 (The Beta Distribution)
dbeta(x, shape1, shape2, ncp = 0, log = FALSE)
pbeta(q, shape1, shape2, ncp = 0, lower.tail = TRUE, log.p = FALSE)
qbeta(p, shape1, shape2, ncp = 0, lower.tail = TRUE, log.p = FALSE)
rbeta(n, shape1, shape2, ncp = 0)

ガンマ分布 (The Gamma Distribution)

dgamma(x, shape, rate = 1, scale = 1/rate, log = FALSE)
pgamma(q, shape, rate = 1, scale = 1/rate, lower.tail = TRUE, log.p = FALSE)
qgamma(p, shape, rate = 1, scale = 1/rate, lower.tail = TRUE, log.p = FALSE)
rgamma(n, shape, rate = 1, scale = 1/rate)

ワイブル分布 (The Weibull Distribution)

dweibull(x, shape, scale = 1, log = FALSE)
pweibull(q, shape, scale = 1, lower.tail = TRUE, log.p = FALSE)
qweibull(p, shape, scale = 1, lower.tail = TRUE, log.p = FALSE)
rweibull(n, shape, scale = 1)

非心分布を作成する場合は，非心パラメタncp=を指定する。