Chisquare {base} | R Documentation |
dchisq(x, df, ncp=0) pchisq(q, df, ncp=0) qchisq(p, df, ncp=0) 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. |
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) = 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) = exp(-lambda/2) SUM_{r=0}^infty ((lambda/2)^r / r!) dchisq(x, df + 2r)
for x >= 0.
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))