| FDist {base} | R Documentation |
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).
df(x, df1, df2, log = FALSE) pf(q, df1, df2, ncp=0, lower.tail = TRUE, log.p = FALSE) qf(p, df1, df2, lower.tail = TRUE, log.p = FALSE) rf(n, df1, df2)
x, q |
vector of quantiles. |
p |
vector of probabilities. |
n |
number of observations to generate. |
df1, df2 |
degrees of freedom. |
ncp |
non-centrality parameter. |
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]. |
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.
df gives the density,
pf gives the distribution function
qf gives the quantile function, and
rf generates random deviates.
dt for Student's t distribution, the square of which is
(almost) equivalent to the F distribution with df2 = 1.
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