distr6 (version 1.3.6)

FDistributionNoncentral: Noncentral F Distribution Class

Description

Mathematical and statistical functions for the Noncentral F distribution, which is commonly used in ANOVA testing and is the ratio of scaled Chi-Squared distributions.

Value

Returns an R6 object inheriting from class SDistribution.

Constructor

FDistributionNoncentral$new(df1 = 1, df2 = 1, location = 0, decorators = NULL, verbose = FALSE)

Constructor Arguments

Argument	Type	Details
df1, df2	numeric	degrees of freedom.
location	numeric	location (ncp in rstats).

decorators Decorator decorators to add functionality. See details.

Constructor Details

The Noncentral F distribution is parameterised with df1 and df2 as positive numerics, location as non-negative numeric.

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 F distribution parameterised with two degrees of freedom parameters, $\mu ,\nu$, and location, $\lambda$, is defined by the pdf, $$f(x)=\sum _{r=0}^{\mathrm{\infty }}((exp(-\lambda /2)(\lambda /2{)}^r)/(B(\nu /2,\mu /2+r)r!))(\mu /\nu {)}^{\mu /2+r}(\nu /(\nu +x\mu ){)}^{(\mu +\nu )/2+r}{x}^{\mu /2-1+r}$$ for $\mu ,\nu >0,\lambda \ge 0$.

The distribution is supported on the Positive Reals.

skewness, kurtosis, entropy, mode, mgf and cf 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, ChiSquared and FDistribution for the Normal, Chi-Squared and central F distributions. CoreStatistics for numerical results.

Examples

# NOT RUN {
x <- FDistributionNoncentral$new(df1 = 1, df2 = 3, location = 2)

# Update parameters
x$setParameterValue(df2 = 10)
x$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)

# }