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. |
df degrees of freedom and
optional non-centrality parameter ncp.
The chi-square distribution with df= n degrees of freedom
has density
f(x) = 1 / (2^(n/2) Gamma(n/2)) x^(n/2-1) e^(-x/2)
for x > 0.
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^r / 2^r r!)pchisq(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 dchisq(x, df=2) == dexp(x, 1/2) pchisq(x, df=2) == pexp(x, 1/2)#- only approximately