Geometric: Geometric Distribution Class

Description

Mathematical and statistical functions for the Geometric distribution, which is commonly used to model the number of trials (or number of failures) before the first success.

Value

Returns an R6 object inheriting from class SDistribution.

Constructor

Geometric$new(prob = 0.5, qprob = NULL, trials = FALSE, decorators = NULL, verbose = FALSE)

Constructor Arguments

Argument	Type	Details
`prob`	numeric	probability of success.
`qprob`	numeric	probability of failure.
`trials`	logical	number of trials or failures, see details.

decorators Decorator decorators to add functionality. See details.

Constructor Details

The Geometric distribution is parameterised with prob or qprob as a number between 0 and 1. These are related via, $$qprob = 1 - prob$$ If qprob is given then prob is ignored. The logical parameter trials determines which Geometric distribution is constructed and cannot be changed after construction. If trials is TRUE then the Geometric distribution that models the number of trials, $x$, before the first success is constructed. Otherwise the Geometric distribution calculates the probability of $y$ failures before the first success. Mathematically these are related by $Y = X - 1$.

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 Geometric distribution parameterised with probability of success, $p$, is defined by the pmf, $$f(x) = (1 - p)^{k-1}p$$ for $p \epsilon [0,1]$.

The distribution is supported on the Naturals (zero is included if modelling number of failures before success)..

The Geometric distribution is used to either refer to modelling the number of trials or number of failures before the first success.

References

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

Examples

Run this code

# NOT RUN {
# Different parameterisations
Geometric$new(prob = 0.2)
Geometric$new(qprob = 0.7)

# Different forms of the distribution
Geometric$new(trials = TRUE) # Number of trials before first success
Geometric$new(trials = FALSE) # Number of failures before first success

# Use description to see which form is used
Geometric$new(trials = TRUE)$description
Geometric$new(trials = FALSE)$description

# Default is prob = 0.5 and number of failures before first success
x <- Geometric$new()

# Update parameters
# When any parameter is updated, all others are too!
x$setParameterValue(qprob = 0.2)
x$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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