InverseGamma: Inverse Gamma Distribution Class

Description

Mathematical and statistical functions for the Inverse Gamma distribution, which is commonly used in Bayesian statistics as the posterior distribution from the unknown variance in a Normal distribution.

Value

Returns an R6 object inheriting from class SDistribution.

Constructor

InverseGamma$new(shape = 1, scale = 1, decorators = NULL, verbose = FALSE)

Constructor Arguments

Argument	Type	Details
`shape`	numeric	shape parameter.
`scale`	numeric	scale parameter.

decorators Decorator decorators to add functionality. See details.

Constructor Details

The Inverse Gamma distribution is parameterised with shape and scale as positive 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 Inverse Gamma distribution parameterised with shape, $\alpha$, and scale, $\beta$, is defined by the pdf, $$f(x) = (\beta^\alpha)/\Gamma(\alpha)x^{-\alpha-1}exp(-\beta/x)$$ for $\alpha, \beta > 0$, where $\Gamma$ is the gamma function.

The distribution is supported on the Positive Reals.

cf is omitted as no closed form analytic expression could be found, decorate with CoreStatistics for numerical results.

The distribution is implemented by interfacing the extraDistr package.

References

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

Examples

Run this code

# NOT RUN {
x  = InverseGamma$new(shape = 1, scale = 4)

# Update parameters
# When any parameter is updated, all others are too!
x$setParameterValue(scale = 2)
x$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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