| Chisquare {base} | R Documentation |
Density, distribution function, quantile function and random
generation for the chi-squared (chi^2) distribution with
df degrees of freedom and optional non-centrality parameter
ncp.
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)
x, q |
vector of quantiles. |
p |
vector of probabilities. |
n |
number of observations to generate. |
df |
degrees of freedom. |
ncp |
non-centrality parameter. For rnchisq, ncp=0
is the only possible value. |
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 chi-squared distribution with df= n degrees of
freedom has density
f_n(x) = 1 / (2^(n/2) Gamma(n/2)) x^(n/2-1) e^(-x/2)
for x > 0. The mean and variance are n and 2n.
The non-central chi-squared distribution with df= n
degrees of freedom and non-centrality parameter ncp
= λ has density
f(x) = exp(-lambda/2) SUM_{r=0}^infty ((lambda/2)^r / r!) dchisq(x, df + 2r)
for x >= 0. It is the distribution of the sum of squares of n normals each with variance one, λ being the sum of squares of the normal means.
dchisq gives the density, pchisq gives the distribution
function, qchisq gives the quantile function, and rchisq
generates random deviates.
dgamma for the Gamma distribution which generalizes the
chi-squared one.
dchisq(1, df=1:3) pchisq(1, df= 3) pchisq(1, df= 3, ncp = 0:4)# includes the above x <- 1:10 ## Chi-squared(df = 2) is a special exponential distribution all.equal(dchisq(x, df=2), dexp(x, 1/2)) all.equal(pchisq(x, df=2), pexp(x, 1/2))