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")