Chisq-class

0th

Percentile

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

ChisqParameter-class AbscontDistribution-class Reals-class rchisq

Aliases
• Chisq-class
• Chisq
• initialize,Chisq-method
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.
as(C0,"Gammad")