Chisq-class {distr} | R Documentation |

## 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.

### 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")
```

*distr*version 2.9.3 Index]