Chisq-class

From distr v2.6
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.

Slots

img
Object of class "Reals": The space of the image of this distribution has got dimension 1 and the name "Real Space".
param
Object of class "ChisqParameter": the parameter of this distribution (df and ncp), declared at its instantiation
r
Object of class "function": generates random numbers (calls function rchisq)
d
Object of class "function": density function (calls function dchisq)
p
Object of class "function": cumulative function (calls function pchisq)
q
Object of class "function": inverse of the cumulative function (calls function qchisq)
.withArith
logical: used internally to issue warnings as to interpretation of arithmetics
.withSim
logical: used internally to issue warnings as to accuracy
.logExact
logical: used internally to flag the case where there are explicit formulae for the log version of density, cdf, and quantile function
.lowerExact
logical: used internally to flag the case where there are explicit formulae for the lower tail version of cdf and quantile function
Symmetry
object of class "DistributionSymmetry"; used internally to avoid unnecessary calculations.

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.

Methods

initialize
signature(.Object = "Chisq"): initialize method
df
signature(object = "Chisq"): returns the slot df of the parameter of the distribution
df<-
signature(object = "Chisq"): modifies the slot df of the parameter of the distribution
ncp
signature(object = "Chisq"): returns the slot ncp of the parameter of the distribution
ncp<-
signature(object = "Chisq"): modifies the slot ncp of the parameter of the distribution
+
signature(e1 = "Chisq", e2 = "Chisq"): For the chi-squared distribution we use its closedness under convolutions.

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.