distr6 (version 1.3.6)

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 mode(which = "all") mode

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.

See Also

listDistributions for all available distributions.

Examples

# 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)

# }