Mathematical and statistical functions for the Discrete Uniform distribution, which is commonly used as a discrete variant of the more popular Uniform distribution, used to model events with an equal probability of occurring (e.g. role of a die).

## Value

Returns an R6 object inheriting from class SDistribution.

## Details

The Discrete Uniform distribution parameterised with lower, $$a$$, and upper, $$b$$, limits is defined by the pmf, $$f(x) = 1/(b - a + 1)$$ for $$a, b \ \in \ Z; \ b \ge a$$.

## Distribution support

The distribution is supported on $$\{a, a + 1,..., b\}$$.

## Default Parameterisation

DUnif(lower = 0, upper = 1)

N/A

N/A

## References

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

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

Other univariate distributions: Arcsine, Arrdist, Bernoulli, BetaNoncentral, Beta, Binomial, Categorical, Cauchy, ChiSquaredNoncentral, ChiSquared, Degenerate, Empirical, Erlang, Exponential, FDistributionNoncentral, FDistribution, Frechet, Gamma, Geometric, Gompertz, 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 -> DiscreteUniform

## 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.

## Active bindings

properties

Returns distribution properties, including skewness type and symmetry.

## Methods

Inherited methods

### Method new()

Creates a new instance of this R6 class.

#### 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).

#### Arguments

...

Unused.

### Method skewness()

The skewness of a distribution is defined by the third standardised moment, $$sk_X = E_X[\frac{x - \mu}{\sigma}^3]$$ 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.

#### 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.

#### Arguments

t

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

...

Unused.

### Method 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.

#### 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

DiscreteUniform\$clone(deep = FALSE)

#### Arguments

deep

Whether to make a deep clone.