distr6 (version 1.3.6)

StudentT: Student's T Distribution Class

Description

Mathematical and statistical functions for the Student's T distribution, which is commonly used to estimate the mean of populations with unknown variance from a small sample size, as well as in t-testing for difference of means and regression analysis.

Value

Returns an R6 object inheriting from class SDistribution.

Constructor

StudentT$new(df = 1, decorators = NULL, verbose = FALSE)

Constructor Arguments

Argument	Type	Details
df	numeric	degrees of freedom.

decorators Decorator decorators to add functionality. See details.

Constructor Details

The Student's T distribution is parameterised with df as a positive 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 Student's T distribution parameterised with degrees of freedom, \(\nu\), is defined by the pdf, $$f(x) = \Gamma((\nu+1)/2)/(\sqrt(\nu\pi)\Gamma(\nu/2)) * (1+(x^2)/\nu)^(-(\nu+1)/2)$$ for \(\nu > 0\).

The distribution is supported on the Reals.

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, StudentTNoncentral for the noncentral Student's T distribution.

Examples

# NOT RUN {
x = StudentT$new(df = 2)

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

# }