R: Class "Chisq"

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)

`.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.

### 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@uni-oldenburg.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.
    ## 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")

[Package distr version 2.8.0 Index]