StudentTNoncentral: Noncentral Student's T Distribution Class

Description

Mathematical and statistical functions for the Noncentral 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

StudentTNoncentral$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 Student's T distribution is parameterised with df as positive numeric and location as real 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 Student's T distribution parameterised with degrees of freedom, $\nu$ and location, $\lambda$, is defined by the pdf, $$f(x) = (\nu^{\nu/2}exp(-(\nu\lambda^2)/(2(x^2+\nu)))/(\sqrt{\pi} \Gamma(\nu/2) 2^{(\nu-1)/2} (x^2+\nu)^{(\nu+1)/2}))\int_{0}^{\infty} y^\nu exp(-1/2(y-x\lambda/\sqrt{x^2+\nu})^2)$$ for $\nu > 0$, $\lambda \epsilon R$.

The distribution is supported on the Reals.

skewness, kurtosis, mode, entropy, pgf, 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.

Examples

Run this code

# NOT RUN {
x = StudentTNoncentral$new(df = 2, location = 3)

# 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)

# }

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