| Chisquare {base} | R Documentation |
The (non-central) Chi-Square Distribution
Description
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.
Usage
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)
Arguments
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
|
Details
The chi-square distribution with df= n degrees of freedom
has density
f_n(x) = \frac{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 =
\lambda has density
f(x) = e^{-\lambda / 2}
\sum_{r=0}^\infty \frac{(\lambda/2)^r}{r!}\, f_{n + 2r}(x)
for x \ge 0.
Value
dchisq gives the density, pchisq gives the distribution
function, qchisq gives the quantile function, and rchisq
generates random deviates.
See Also
dgamma for the Gamma distribution which generalizes the
chi-square one.
Examples
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))