Chisq-class
Class "Chisq"
The chi-squared 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 $x > 0$. The mean and variance are $n$ and $2n$.
The non-central chi-squared 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 $x \ge 0$. For integer $n$, this is the distribution of
the sum of squares of $n$ normals each with variance one,
$\lambda$ being the sum of squares of the normal means.
C.f. rchisq
- Keywords
- distribution
Note
Warning: The code for pchisq and qchisq is unreliable for values of ncp above approximately 290.
Objects from the Class
Objects can be created by calls of the form Chisq(df, ncp).
This object is a chi-squared distribution.
Extends
Class "ExpOrGammaOrChisq", directly.
Class "AbscontDistribution", by class "ExpOrGammaOrChisq".
Class "UnivariateDistribution", by class "AbscontDistribution".
Class "Distribution", by class "UnivariateDistribution".
Is-Relations
By means of setIs, R ``knows'' that a distribution object obj of class "Chisq" with non-centrality 0 also is
a Gamma distribution with parameters shape = df(obj)/2, scale = 2.
concept
- absolutely continuous distribution
- Chi square distribution
- S4 distribution class
- generating function
See Also
ChisqParameter-class
AbscontDistribution-class
Reals-class
rchisq
Examples
C <- Chisq(df = 1, ncp = 1) # C is a chi-squared distribution with df=1 and ncp=1.
r(C)(1) # one random number generated from this distribution, e.g. 0.2557184
d(C)(1) # Density of this distribution is 0.2264666 for x = 1.
p(C)(1) # Probability that x < 1 is 0.4772499.
q(C)(.1) # Probability that x < 0.04270125 is 0.1.
df(C) # df of this distribution is 1.
df(C) <- 2 # df of this distribution is now 2.
is(C, "Gammad") # no
C0 <- Chisq() # default: Chisq(df=1,ncp=0)
is(C0, "Gammad") # yes
as(C0,"Gammad")