Geometric | R Documentation |

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.

The Geometric distribution parameterised with probability of success, *p*, is defined by the pmf,

*f(x) = (1 - p)^{k-1}p*

for probability *p*.

The Geometric distribution is used to either model the number of trials
(`trials = TRUE`

) or number of failures (`trials = FALSE`

) before the first success.

Returns an R6 object inheriting from class SDistribution.

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

Geom(prob = 0.5, trials = FALSE)

N/A

N/A

`distr6::Distribution`

-> `distr6::SDistribution`

-> `Geometric`

`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.

`new()`

Creates a new instance of this R6 class.

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

`prob`

`(numeric(1))`

Probability of success.`qprob`

`(numeric(1))`

Probability of failure. If provided then`prob`

is ignored.`qprob = 1 - prob`

.`trials`

`(logical(1))`

If`TRUE`

then the distribution models the number of trials,*x*, before the first success. Otherwise the distribution calculates the probability of*y*failures before the first success. Mathematically these are related by*Y = X - 1*.`decorators`

`(character())`

Decorators to add to the distribution during construction.

`mean()`

The arithmetic mean of a (discrete) probability distribution X is the expectation

*E_X(X) = ∑ p_X(x)*x*

with an integration analogue for continuous distributions.

Geometric$mean(...)

`...`

Unused.

`mode()`

The mode of a probability distribution is the point at which the pdf is a local maximum, a distribution can be unimodal (one maximum) or multimodal (several maxima).

Geometric$mode(which = "all")

`which`

`(character(1) | numeric(1)`

Ignored if distribution is unimodal. Otherwise`"all"`

returns all modes, otherwise specifies which mode to return.

`variance()`

The variance of a distribution is defined by the formula

*var_X = E[X^2] - E[X]^2*

where *E_X* is the expectation of distribution X. If the distribution is multivariate the
covariance matrix is returned.

Geometric$variance(...)

`...`

Unused.

`skewness()`

The skewness of a distribution is defined by the third standardised moment,

*sk_X = E_X[((x - μ)/σ)^3]*

where *E_X* is the expectation of distribution X, *μ* is the mean of the
distribution and *σ* is the standard deviation of the distribution.

Geometric$skewness(...)

`...`

Unused.

`kurtosis()`

The kurtosis of a distribution is defined by the fourth standardised moment,

*k_X = E_X[((x - μ)/σ)^4]*

where *E_X* is the expectation of distribution X, *μ* is the mean of the
distribution and *σ* is the standard deviation of the distribution.
Excess Kurtosis is Kurtosis - 3.

Geometric$kurtosis(excess = TRUE, ...)

`excess`

`(logical(1))`

If`TRUE`

(default) excess kurtosis returned.`...`

Unused.

`entropy()`

The entropy of a (discrete) distribution is defined by

*- ∑ (f_X)log(f_X)*

where *f_X* is the pdf of distribution X, with an integration analogue for
continuous distributions.

Geometric$entropy(base = 2, ...)

`base`

`(integer(1))`

Base of the entropy logarithm, default = 2 (Shannon entropy)`...`

Unused.

`mgf()`

The moment generating function is defined by

*mgf_X(t) = E_X[exp(xt)]*

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

Geometric$mgf(t, ...)

`t`

`(integer(1))`

t integer to evaluate function at.`...`

Unused.

`cf()`

The characteristic function is defined by

*cf_X(t) = E_X[exp(xti)]*

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

Geometric$cf(t, ...)

`t`

`(integer(1))`

t integer to evaluate function at.`...`

Unused.

`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.

Geometric$pgf(z, ...)

`z`

`(integer(1))`

z integer to evaluate probability generating function at.`...`

Unused.

`clone()`

The objects of this class are cloneable with this method.

Geometric$clone(deep = FALSE)

`deep`

Whether to make a deep clone.

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

Other discrete distributions:
`Bernoulli`

,
`Binomial`

,
`Categorical`

,
`Degenerate`

,
`DiscreteUniform`

,
`EmpiricalMV`

,
`Empirical`

,
`Hypergeometric`

,
`Logarithmic`

,
`Matdist`

,
`Multinomial`

,
`NegativeBinomial`

,
`WeightedDiscrete`

Other univariate distributions:
`Arcsine`

,
`Bernoulli`

,
`BetaNoncentral`

,
`Beta`

,
`Binomial`

,
`Categorical`

,
`Cauchy`

,
`ChiSquaredNoncentral`

,
`ChiSquared`

,
`Degenerate`

,
`DiscreteUniform`

,
`Empirical`

,
`Erlang`

,
`Exponential`

,
`FDistributionNoncentral`

,
`FDistribution`

,
`Frechet`

,
`Gamma`

,
`Gompertz`

,
`Gumbel`

,
`Hypergeometric`

,
`InverseGamma`

,
`Laplace`

,
`Logarithmic`

,
`Logistic`

,
`Loglogistic`

,
`Lognormal`

,
`Matdist`

,
`NegativeBinomial`

,
`Normal`

,
`Pareto`

,
`Poisson`

,
`Rayleigh`

,
`ShiftedLoglogistic`

,
`StudentTNoncentral`

,
`StudentT`

,
`Triangular`

,
`Uniform`

,
`Wald`

,
`Weibull`

,
`WeightedDiscrete`

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