# Gompertz: Gompertz Distribution Class In distr6: The Complete R6 Probability Distributions Interface

## Description

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

## Details

The Gompertz distribution parameterised with shape, α, and scale, β, is defined by the pdf,

f(x) = αβ exp(xβ)exp(α)exp(-exp(xβ)α)

for α, β > 0.

## Value

Returns an R6 object inheriting from class SDistribution.

## Distribution support

The distribution is supported on the Non-Negative Reals.

## Default Parameterisation

Gomp(shape = 1, scale = 1)

N/A

N/A

## Super classes

`distr6::Distribution` -> `distr6::SDistribution` -> `Gompertz`

## Public fields

`name`

Full name of distribution.

`short_name`

Short name of distribution for printing.

`description`

Brief description of the distribution.

`packages`

Packages required to be installed in order to construct the distribution.

## Methods

#### Public methods

Inherited methods

#### Method `new()`

Creates a new instance of this R6 class.

##### Usage
`Gompertz\$new(shape = NULL, scale = NULL, decorators = NULL)`
##### Arguments
`shape`

`(numeric(1))`
Shape parameter, defined on the positive Reals.

`scale`

`(numeric(1))`
Scale parameter, defined on the positive Reals.

`decorators`

`(character())`
Decorators to add to the distribution during construction.

#### Method `median()`

Returns the median of the distribution. If an analytical expression is available returns distribution median, otherwise if symmetric returns `self\$mean`, otherwise returns `self\$quantile(0.5)`.

##### Usage
`Gompertz\$median()`

#### Method `pgf()`

The probability generating function is defined by

pgf_X(z) = E_X[exp(z^x)]

where X is the distribution and E_X is the expectation of the distribution X.

##### Usage
`Gompertz\$pgf(z, ...)`
##### Arguments
`z`

`(integer(1))`
z integer to evaluate probability generating function at.

`...`

Unused.

#### Method `clone()`

The objects of this class are cloneable with this method.

##### Usage
`Gompertz\$clone(deep = FALSE)`
##### Arguments
`deep`

Whether to make a deep clone.

## References

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

Other continuous distributions: `Arcsine`, `BetaNoncentral`, `Beta`, `Cauchy`, `ChiSquaredNoncentral`, `ChiSquared`, `Dirichlet`, `Erlang`, `Exponential`, `FDistributionNoncentral`, `FDistribution`, `Frechet`, `Gamma`, `Gumbel`, `InverseGamma`, `Laplace`, `Logistic`, `Loglogistic`, `Lognormal`, `MultivariateNormal`, `Normal`, `Pareto`, `Poisson`, `Rayleigh`, `ShiftedLoglogistic`, `StudentTNoncentral`, `StudentT`, `Triangular`, `Uniform`, `Wald`, `Weibull`
Other univariate distributions: `Arcsine`, `Bernoulli`, `BetaNoncentral`, `Beta`, `Binomial`, `Categorical`, `Cauchy`, `ChiSquaredNoncentral`, `ChiSquared`, `Degenerate`, `DiscreteUniform`, `Empirical`, `Erlang`, `Exponential`, `FDistributionNoncentral`, `FDistribution`, `Frechet`, `Gamma`, `Geometric`, `Gumbel`, `Hypergeometric`, `InverseGamma`, `Laplace`, `Logarithmic`, `Logistic`, `Loglogistic`, `Lognormal`, `NegativeBinomial`, `Normal`, `Pareto`, `Poisson`, `Rayleigh`, `ShiftedLoglogistic`, `StudentTNoncentral`, `StudentT`, `Triangular`, `Uniform`, `Wald`, `Weibull`, `WeightedDiscrete`