distr6 (version 1.3.6)

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.

Value

Returns an R6 object inheriting from class SDistribution.

Constructor

ChiSquaredNoncentral$new(df = 1, location = 0, decorators = NULL, verbose = FALSE)

Constructor Arguments

Argument	Type	Details
df	numeric	degrees of freedom.
location	numeric	location (ncp in rstats).

decorators Decorator decorators to add functionality. See details.

Constructor Details

The Noncentral Chi-Squared distribution is parameterised with df and location as non-negative numerics.

Public Variables

Variable	Return
name	Name of distribution.
short_name	Id of distribution.
description	Brief description of distribution.

Public Methods

Accessor Methods	Link
decorators	decorators
traits	traits
valueSupport	valueSupport
variateForm	variateForm
type	type
properties	properties
support	support
symmetry	symmetry
sup	sup
inf	inf
dmax	dmax
dmin	dmin
skewnessType	skewnessType
kurtosisType	kurtosisType

Statistical Methods Link pdf(x1, ..., log = FALSE, simplify = TRUE) pdf cdf(x1, ..., lower.tail = TRUE, log.p = FALSE, simplify = TRUE) cdf quantile(p, ..., lower.tail = TRUE, log.p = FALSE, simplify = TRUE) quantile.Distribution rand(n, simplify = TRUE) rand mean() mean.Distribution variance() variance stdev() stdev prec() prec cor() cor skewness() skewness kurtosis(excess = TRUE) kurtosis entropy(base = 2) entropy mgf(t) mgf cf(t) cf pgf(z) pgf median() median.Distribution iqr() iqr mode(which = "all") mode

Parameter Methods Link parameters(id) parameters getParameterValue(id, error = "warn") getParameterValue setParameterValue(..., lst = NULL, error = "warn") setParameterValue

Validation Methods Link liesInSupport(x, all = TRUE, bound = FALSE) liesInSupport liesInType(x, all = TRUE, bound = FALSE) liesInType

Representation Methods Link strprint(n = 2) strprint print(n = 2) print summary(full = T) summary.Distribution

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 \(\nu \ge 0\), \(\lambda \ge 0\).

The distribution is supported on the Positive Reals.

entropy and mode are omitted as no closed form analytic expression could be found, decorate with CoreStatistics for numerical results.

References

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

See Also

listDistributions for all available distributions. Normal for the Normal distribution, ChiSquared for the central Chi-Squared distribution. CoreStatistics for numerical results.

Examples

# NOT RUN {
x = ChiSquaredNoncentral$new(df = 2, location = 2)

# Update parameters
x$setParameterValue(location = 3)
x$parameters()

# d/p/q/r
x$pdf(5)
x$cdf(5)
x$quantile(0.42)
x$rand(4)

# Statistics
x$mean()
x$variance()

summary(x)

# }