F分布是1924年英國統計學家Ronald.A.Fisher爵士提出，并以其姓氏的第一個字母命名的。它是兩個服從卡方分布的獨立隨機變量各除以其自由度后的比值的抽樣分布，是一種非對稱分布，且位置不可互換。F分布有著廣泛的應用，如在方差分析、回歸方程的顯著性檢驗中都有著重要的地位。

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The F Distribution

Description

Density, distribution function, quantile function and random generation for the F distribution with?df1?and?df2?degrees of freedom (and optional non-centrality parameter?ncp).

Usage

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)

Arguments

x, q	vector of quantiles.
p	vector of probabilities.
n	number of observations. If?length(n) > 1, the length is taken to be the number required.
df1, df2	degrees of freedom.?Inf?is allowed.
ncp	non-centrality parameter. If omitted the central F is assumed.
log, log.p	logical; if TRUE, probabilities p are given as log(p).
lower.tail	logical; if TRUE (default), probabilities are?P[X ≤ x], otherwise,?P[X > x].

####F分布 # 1.F分布中抽樣函數rf # location：x0; scale:gamma n = 100 df1 <- 10 df2 <-20 rf(n, df1, df2)# 2.F分布概率密度函數 x <- seq(0,10,0.1) y <- df(x,df1, df2) plot(x,y)# 3.F分布累積概率 # x <- seq(1,20,0.1) # plot(x,df(x,df1, df2)) # P[X ≤ x] pf(1,df1=df1, df2=df2) # P[X > x] pf(1,df1=df1, df2=df2,lower.tail = FALSE)# probabilities p are given as log(p). pf(1,df1=df1, df2=df2,log.p = TRUE)# 4.qf函數(pf的反函數) # 累積概率為0.95時的x值 # x <- seq(-10,10,0.1) # plot(x,pf(x,df1=df1, df2=df2)) qf(0.95, df1=df1, df2=df2) qf(0.995, df1=df1, df2=df2)

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