Gamma: Gamma Distribution Class

Description

Mathematical and statistical functions for the Gamma distribution, which is commonly used as the prior in Bayesian modelling, the convolution of exponential distributions, and to model waiting times.

Value

Returns an R6 object inheriting from class SDistribution.

Constructor

Gamma$new(shape = 1, rate = 1, scale = NULL, mean = NULL, decorators = NULL, verbose = FALSE)

Constructor Arguments

Argument	Type	Details
`shape`	numeric	shape parameter.
`rate`	numeric	inverse scale parameter.
`scale`	numeric	scale parameter.
`mean`	numeric	alternate scale parameter.

decorators Decorator decorators to add functionality. See details.

Constructor Details

The Gamma distribution is parameterised with shape and either rate, scale or mean, all as positive numerics. These are related via, $$scale = 1/rate$$ $$mean = shape/rate$$ If mean is given then rate and scale are ignored. If scale is given then rate is ignored.

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`



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 Gamma distribution parameterised with shape, $\alpha$, and rate, $\beta$, is defined by the pdf, $$f(x) = (\beta^\alpha)/\Gamma(\alpha)x^{\alpha-1}exp(-x\beta)$$ for $\alpha, \beta > 0$.

The distribution is supported on the Positive Reals.

References

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

Examples

Run this code

# NOT RUN {
Gamma$new(shape = 1, rate = 2)
Gamma$new(shape = 1, scale = 4)
Gamma$new(shape = 1, mean = 0.5)

# Default is shape = 1, rate = 1
x = Gamma$new(verbose = TRUE)

# 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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