| Chisquare {base} | R Documentation |
Density, distribution function, quantile function and random
generation for the chi-square (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)
x, q |
vector of quantiles. |
p |
vector of probabilities. |
n |
number of observations to generate. |
df |
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 chi-square 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. Mean and variance are n and 2n, respectively.
The non-central chi-square 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.
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-square one.
dchisq(1, df=1:3) pchisq(1, df= 3) pchisq(1, df= 3, ncp = 0:4)# includes the above x <- 1:10 ## Chisquare( 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))