Gompertz: Gompertz Distribution Class

Description

Mathematical and statistical functions for the Gompertz distribution, which is commonly used in survival analysis particularly to model adult mortality rates..

Value

Returns an R6 object inheriting from class SDistribution.

Constructor

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

Constructor Arguments

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

decorators Decorator decorators to add functionality. See details.

Constructor Details

The Gompertz 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`



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 Gompertz distribution parameterised with shape, $\alpha$, and scale, $\beta$, is defined by the pdf, $$f(x) = \alpha\beta exp(x\beta)exp(\alpha)exp(-exp(x\beta)\alpha)$$ for $\alpha, \beta > 0$.

The distribution is supported on the Non-Negative Reals.

mean, var, mgf, cf, entropy, skewness and kurtosis are omitted as no closed form analytic expression could be found, decorate with CoreStatistics for numerical results.

Unfortunately the Gompertz distribution is quite complex to deal with and as such no closed form expressions exist for its mathematical and statistical properties.

References

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

Examples

Run this code

# NOT RUN {
x <- Gompertz$new(shape = 2, scale = 3)

# Update parameters
x$setParameterValue(scale = 1)
x$parameters()

# d/p/q/r
x$pdf(5)
x$cdf(5)
x$quantile(0.42)
x$rand(4)

summary(x)

# }

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