distr (version 2.9.5)

Chisq-class: Class "Chisq"

Description

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

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.

Author

Thomas Stabla ,
Florian Camphausen ,
Peter Ruckdeschel ,
Matthias Kohl

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.
## in RStudio or Jupyter IRKernel, use q.l(.)(.) instead of q(.)(.)
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")