Chisq-class {distr}R Documentation

Class "Chisq"

Description

The chi-squared distribution with df= n degrees of freedom has density

f_n(x) = 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 = λ has density

f(x) = exp(-lambda/2) SUM_{r=0}^infty ((lambda/2)^r / r!) dchisq(x, df + 2r)

for x >= 0. For integer n, this is the distribution of the sum of squares of n normals each with variance one, λ 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)

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.

Note

Warning: The code for pchisq and qchisq is unreliable for values of ncp above approximately 290.

Author(s)

Thomas Stabla statho3@web.de,
Florian Camphausen fcampi@gmx.de,
Peter Ruckdeschel Peter.Ruckdeschel@itwm.fraunhofer.de,
Matthias Kohl Matthias.Kohl@stamats.de

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")

[Package distr version 2.0.6 Index]