Gompertz Distribution Class

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.

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 \(\alpha, \beta > 0\).

Distribution support

The distribution is supported on the Non-Negative Reals.

Default Parameterisation

Gomp(shape = 1, scale = 1)

Omitted Methods

N/A

Also known as

N/A

References

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

See also

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, Arrdist, 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, Matdist, NegativeBinomial, Normal, Pareto, Poisson, Rayleigh, ShiftedLoglogistic, StudentTNoncentral, StudentT, Triangular, Uniform, Wald, Weibull, WeightedDiscrete

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.

alias

Alias of the distribution.

packages

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

Methods

Public methods

• Gompertz$new()

• Gompertz$median()

• Gompertz$pgf()

• Gompertz$clone()

Inherited methods

• distr6::Distribution$cdf()
• distr6::Distribution$confidence()
• distr6::Distribution$correlation()
• distr6::Distribution$getParameterValue()
• distr6::Distribution$iqr()
• distr6::Distribution$liesInSupport()
• distr6::Distribution$liesInType()
• distr6::Distribution$parameters()
• distr6::Distribution$pdf()
• distr6::Distribution$prec()
• distr6::Distribution$print()
• distr6::Distribution$quantile()
• distr6::Distribution$rand()
• distr6::Distribution$setParameterValue()
• distr6::Distribution$stdev()
• distr6::Distribution$strprint()
• distr6::Distribution$summary()
• distr6::Distribution$workingSupport()

---

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.

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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()

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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.

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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.