distr6 (version 1.6.2)

Bernoulli: Bernoulli Distribution Class

Description

Mathematical and statistical functions for the Bernoulli distribution, which is commonly used to model a two-outcome scenario.

Value

Returns an R6 object inheriting from class SDistribution.

Distribution support

The distribution is supported on $\{0,1\}$.

Default Parameterisation

Bern(prob = 0.5)

Omitted Methods

N/A

Also known as

N/A

Super classes

distr6::Distribution -> distr6::SDistribution -> Bernoulli

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.

Active bindings

properties

Returns distribution properties, including skewness type and symmetry.

Methods

Public methods

• Bernoulli$new()

• Bernoulli$mean()

• Bernoulli$mode()

• Bernoulli$median()

• Bernoulli$variance()

• Bernoulli$skewness()

• Bernoulli$kurtosis()

• Bernoulli$entropy()

• Bernoulli$mgf()

• Bernoulli$cf()

• Bernoulli$pgf()

• Bernoulli$clone()

• distr6::Distribution$cdf()

• 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

Bernoulli$new(prob = NULL, qprob = NULL, decorators = NULL)

Arguments

prob

(numeric(1)) Probability of success.

qprob

(numeric(1)) Probability of failure. If provided then prob is ignored. qprob = 1 - prob.

decorators

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

Method mean()

The arithmetic mean of a (discrete) probability distribution X is the expectation $$E_X(X)=\sum p_X(x)\ast x$$ with an integration analogue for continuous distributions.

Usage

Bernoulli$mean(...)

Arguments

...

Unused.

Method 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).

Usage

Bernoulli$mode(which = "all")

Arguments

which

(character(1) | numeric(1) Ignored if distribution is unimodal. Otherwise "all" returns all modes, otherwise specifies which mode to return.

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

Bernoulli$median()

Method variance()

The variance of a distribution is defined by the formula $$va{r}_X=E[X^2]-E[X{]}^2$$ where $E_X$ is the expectation of distribution X. If the distribution is multivariate the covariance matrix is returned.

Usage

Bernoulli$variance(...)

Arguments

...

Unused.

Method skewness()

The skewness of a distribution is defined by the third standardised moment, $$s{k}_X=E_X[{\frac{x-\mu }{\sigma }}^3]$$ where $E_X$ is the expectation of distribution X, $\mu$ is the mean of the distribution and $\sigma$ is the standard deviation of the distribution.

Usage

Bernoulli$skewness(...)

Arguments

...

Unused.

Method kurtosis()

The kurtosis of a distribution is defined by the fourth standardised moment, $$k_X=E_X[{\frac{x-\mu }{\sigma }}^4]$$ where $E_X$ is the expectation of distribution X, $\mu$ is the mean of the distribution and $\sigma$ is the standard deviation of the distribution. Excess Kurtosis is Kurtosis - 3.

Usage

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

Arguments

excess

(logical(1)) If TRUE (default) excess kurtosis returned.

...

Unused.

Method entropy()

The entropy of a (discrete) distribution is defined by $$-\sum (f_X)log(f_X)$$ where $f_X$ is the pdf of distribution X, with an integration analogue for continuous distributions.

Usage

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

Arguments

base

(integer(1)) Base of the entropy logarithm, default = 2 (Shannon entropy)

...

Unused.

Method mgf()

The moment generating function is defined by $$mg{f}_X(t)=E_X[exp(xt)]$$ where X is the distribution and $E_X$ is the expectation of the distribution X.

Usage

Bernoulli$mgf(t, ...)

Arguments

t

(integer(1)) t integer to evaluate function at.

...

Unused.

Method cf()

The characteristic function is defined by $$c{f}_X(t)=E_X[exp(xti)]$$ where X is the distribution and $E_X$ is the expectation of the distribution X.

Usage

Bernoulli$cf(t, ...)

Arguments

t

(integer(1)) t integer to evaluate function at.

...

Unused.

Method pgf()

The probability generating function is defined by $$pg{f}_X(z)=E_X[exp(z^x)]$$ where X is the distribution and $E_X$ is the expectation of the distribution X.

Usage

Bernoulli$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

Bernoulli$clone(deep = FALSE)

Arguments

deep

Whether to make a deep clone.

Details

The Bernoulli distribution parameterised with probability of success, $p$, is defined by the pmf, $$f(x)=p,ifx=1$$$$f(x)=1-p,ifx=0$$ for probability $p$.

References

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

See Also

Other discrete distributions: Binomial, Categorical, Degenerate, DiscreteUniform, EmpiricalMV, Empirical, Geometric, Hypergeometric, Logarithmic, Multinomial, NegativeBinomial, WeightedDiscrete

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