The F Distribution

Usage

df(x, df1, df2)
pf(q, df1, df2, ncp=0)
qf(p, df1, df2)
rf(n, df1, df2)

Arguments

x,q vector of quantiles.
p vector of probabilities.
n number of observations to generate.
df1,df2 degrees of freedom.
ncp non-centrality parameter.

Value

These functions provide information about the F distribution with df1 and df2 degrees of freedom (and optional non-centrality parameter ncp). df gives the density, pf gives the distribution function qf gives the quantile function and rf generates random deviates.

The F distribution with df1 = n1 and df2 = n2 degrees of freedom has density

f(x) = Gamma((n1 + n2)/2) / (Gamma(n1/2) Gamma(n2/2)) (n1/n2)^(n1/2) x^(n1/2 - 1) (1 + (n1/n2) x)^-(n1 + n2)/2

for x > 0.

See Also

dt for Student's t distribution, the square of which is (almost) equivalent to the F distribution with df2 = 1.

Examples

df(1,1,1) == dt(1,1)# TRUE

## Identity:  qf(2*p -1, 1, df)) == qt(p, df)^2)  for  p >= 1/2
p <- seq(1/2, .99, length=50); df <- 10
rel.err <- function(x,y) ifelse(x==y,0, abs(x-y)/mean(abs(c(x,y))))
quantile(rel.err(qf(2*p -1, df1=1, df2=df), qt(p, df)^2), .90)# ~= 7e-9

[Package Contents]