| Chisquare {base} | R Documentation |
The (non-central) Chi-Square Distribution
Usage
dchisq(x, df, ncp=0)
pchisq(q, df, ncp=0)
qchisq(p, df, ncp=0)
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. |
Value
These functions provide information about the chi-square
(\chi^2) distribution with df degrees of freedom and
optional non-centrality parameter ncp.
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.
dchisq gives the density f_n,
pchisq gives the distribution function F_n, qchisq gives
the quantile function and rchisq generates random deviates.
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.
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))