Learn R Programming

distr6 (version 1.5.6)

ChiSquaredNoncentral: Noncentral Chi-Squared Distribution Class

Description

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

Arguments

Value

Returns an R6 object inheriting from class SDistribution.

Distribution support

The distribution is supported on the Positive Reals.

Default Parameterisation

ChiSqNC(df = 1, location = 0)

Omitted Methods

N/A

Also known as

N/A

Super classes

distr6::Distribution -> distr6::SDistribution -> ChiSquaredNoncentral

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.

Methods

Public methods

Method new()

Creates a new instance of this R6 class.

Usage

ChiSquaredNoncentral$new(df = NULL, location = NULL, decorators = NULL)

Arguments

df

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

location

(numeric(1)) Location parameter, defined on the non-negative 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 $$E_X(X) = \sum p_X(x)*x$$ with an integration analogue for continuous distributions.

Usage

ChiSquaredNoncentral$mean(...)

Arguments

...

Unused.

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

ChiSquaredNoncentral$variance(...)

Arguments

...

Unused.

Method skewness()

The skewness of a distribution is defined by the third standardised moment, $$sk_X = E_X[\frac{x - \mu}{\sigma}^3]$$ where \(E_X\) is the expectation of distribution X, \(\mu\) is the mean of the distribution and \(\sigma\) is the standard deviation of the distribution.

Usage

ChiSquaredNoncentral$skewness(...)

Arguments

...

Unused.

Method kurtosis()

The kurtosis of a distribution is defined by the fourth standardised moment, $$k_X = E_X[\frac{x - \mu}{\sigma}^4]$$ where \(E_X\) is the expectation of distribution X, \(\mu\) is the mean of the distribution and \(\sigma\) is the standard deviation of the distribution. Excess Kurtosis is Kurtosis - 3.

Usage

ChiSquaredNoncentral$kurtosis(excess = TRUE, ...)

Arguments

excess

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

...

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

ChiSquaredNoncentral$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

ChiSquaredNoncentral$cf(t, ...)

Arguments

t

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

...

Unused.

Method setParameterValue()

Sets the value(s) of the given parameter(s).

Usage

ChiSquaredNoncentral$setParameterValue(
  ...,
  lst = NULL,
  error = "warn",
  resolveConflicts = FALSE
)

Arguments

...

ANY Named arguments of parameters to set values for. See examples.

lst

(list(1)) Alternative argument for passing parameters. List names should be parameter names and list values are the new values to set.

error

(character(1)) If "warn" then returns a warning on error, otherwise breaks if "stop".

resolveConflicts

(logical(1)) If FALSE (default) throws error if conflicting parameterisations are provided, otherwise automatically resolves them by removing all conflicting parameters.

Method clone()

The objects of this class are cloneable with this method.

Usage

ChiSquaredNoncentral$clone(deep = FALSE)

Arguments

deep

Whether to make a deep clone.

Details

The Noncentral Chi-Squared distribution parameterised with degrees of freedom, \(\nu\), and location, \(\lambda\), is defined by the pdf, $$f(x) = exp(-\lambda/2) \sum_{r=0}^\infty ((\lambda/2)^r/r!) (x^{(\nu+2r)/2-1}exp(-x/2))/(2^{(\nu+2r)/2}\Gamma((\nu+2r)/2))$$ for \(\nu \ge 0\), \(\lambda \ge 0\).

References

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

See Also

Other continuous distributions: Arcsine, BetaNoncentral, Beta, Cauchy, ChiSquared, Dirichlet, Erlang, Exponential, FDistributionNoncentral, FDistribution, Frechet, Gamma, Gompertz, Gumbel, InverseGamma, Laplace, Logistic, Loglogistic, Lognormal, MultivariateNormal, Normal, Pareto, Poisson, Rayleigh, ShiftedLoglogistic, StudentTNoncentral, StudentT, Triangular, Uniform, Wald, Weibull

Other univariate distributions: Arcsine, Bernoulli, BetaNoncentral, Beta, Binomial, Categorical, Cauchy, ChiSquared, Degenerate, DiscreteUniform, Empirical, Erlang, Exponential, FDistributionNoncentral, FDistribution, Frechet, Gamma, Geometric, Gompertz, Gumbel, Hypergeometric, InverseGamma, Laplace, Logarithmic, Logistic, Loglogistic, Lognormal, NegativeBinomial, Normal, Pareto, Poisson, Rayleigh, ShiftedLoglogistic, StudentTNoncentral, StudentT, Triangular, Uniform, Wald, Weibull, WeightedDiscrete