# ChiSquared: Chi-Squared Distribution Class In distr6: The Complete R6 Probability Distributions Interface

 ChiSquared R Documentation

## Chi-Squared Distribution Class

### Description

Mathematical and statistical functions for the Chi-Squared distribution, which is commonly used to model the sum of independent squared Normal distributions and for confidence intervals.

### Details

The Chi-Squared distribution parameterised with degrees of freedom, ν, is defined by the pdf,

f(x) = (x^{ν/2-1} exp(-x/2))/(2^{ν/2}Γ(ν/2))

for ν > 0.

### Value

Returns an R6 object inheriting from class SDistribution.

### Distribution support

The distribution is supported on the Positive Reals.

ChiSq(df = 1)

N/A

N/A

### Super classes

distr6::Distribution -> distr6::SDistribution -> ChiSquared

### Public fields

name

Full name of distribution.

short_name

Short name of distribution for printing.

description

Brief description of the distribution.

packages

Packages required to be installed in order to construct the distribution.

### Active bindings

properties

Returns distribution properties, including skewness type and symmetry.

### Methods

#### Public methods

Inherited methods

#### Method new()

Creates a new instance of this R6 class.

##### Usage
ChiSquared\$new(df = NULL, decorators = NULL)
##### Arguments
df

(integer(1))
Degrees of freedom of the distribution defined on the positive Reals.

decorators

(character())
Decorators to add to the distribution during construction.

#### Method mean()

The arithmetic mean of a (discrete) probability distribution X is the expectation

E_X(X) = ∑ p_X(x)*x

with an integration analogue for continuous distributions.

##### Usage
ChiSquared\$mean(...)
...

Unused.

#### Method mode()

The mode of a probability distribution is the point at which the pdf is a local maximum, a distribution can be unimodal (one maximum) or multimodal (several maxima).

##### Usage
ChiSquared\$mode(which = "all")
##### Arguments
which

(character(1) | numeric(1)
Ignored if distribution is unimodal. Otherwise "all" returns all modes, otherwise specifies which mode to return.

#### Method variance()

The variance of a distribution is defined by the formula

var_X = E[X^2] - E[X]^2

where E_X is the expectation of distribution X. If the distribution is multivariate the covariance matrix is returned.

##### Usage
ChiSquared\$variance(...)
...

Unused.

#### Method skewness()

The skewness of a distribution is defined by the third standardised moment,

sk_X = E_X[((x - μ)/σ)^3]

where E_X is the expectation of distribution X, μ is the mean of the distribution and σ is the standard deviation of the distribution.

##### Usage
ChiSquared\$skewness(...)
...

Unused.

#### Method kurtosis()

The kurtosis of a distribution is defined by the fourth standardised moment,

k_X = E_X[((x - μ)/σ)^4]

where E_X is the expectation of distribution X, μ is the mean of the distribution and σ is the standard deviation of the distribution. Excess Kurtosis is Kurtosis - 3.

##### Usage
ChiSquared\$kurtosis(excess = TRUE, ...)
##### Arguments
excess

(logical(1))
If TRUE (default) excess kurtosis returned.

...

Unused.

#### Method entropy()

The entropy of a (discrete) distribution is defined by

- ∑ (f_X)log(f_X)

where f_X is the pdf of distribution X, with an integration analogue for continuous distributions.

##### Usage
ChiSquared\$entropy(base = 2, ...)
##### Arguments
base

(integer(1))
Base of the entropy logarithm, default = 2 (Shannon entropy)

...

Unused.

#### Method mgf()

The moment generating function is defined by

mgf_X(t) = E_X[exp(xt)]

where X is the distribution and E_X is the expectation of the distribution X.

##### Usage
ChiSquared\$mgf(t, ...)
##### Arguments
t

(integer(1))
t integer to evaluate function at.

...

Unused.

#### Method cf()

The characteristic function is defined by

cf_X(t) = E_X[exp(xti)]

where X is the distribution and E_X is the expectation of the distribution X.

##### Usage
ChiSquared\$cf(t, ...)
##### Arguments
t

(integer(1))
t integer to evaluate function at.

...

Unused.

#### Method pgf()

The probability generating function is defined by

pgf_X(z) = E_X[exp(z^x)]

where X is the distribution and E_X is the expectation of the distribution X.

##### Usage
ChiSquared\$pgf(z, ...)
##### Arguments
z

(integer(1))
z integer to evaluate probability generating function at.

...

Unused.

#### Method clone()

The objects of this class are cloneable with this method.

##### Usage
ChiSquared\$clone(deep = FALSE)
##### Arguments
deep

Whether to make a deep clone.

### References

McLaughlin, M. P. (2001). A compendium of common probability distributions (pp. 2014-01). Michael P. McLaughlin.