Categorical Distribution Class
Mathematical and statistical functions for the Categorical distribution, which is commonly used in classification supervised learning.
The Categorical distribution parameterised with a given support set, x_1,...,x_k, and respective probabilities, p_1,...,p_k, is defined by the pmf,
f(x_i) = p_i
for p_i, i = 1,…,k; ∑ p_i = 1.
Sampling from this distribution is performed with the sample function with the elements given
as the support set and the probabilities from the probs parameter. The cdf and quantile assumes
that the elements are supplied in an indexed order (otherwise the results are meaningless).
The number of points in the distribution cannot be changed after construction.
Returns an R6 object inheriting from class SDistribution.
The distribution is supported on x_1,...,x_k.
Cat(elements = 1, probs = 1)
N/A
N/A
distr6::Distribution -> distr6::SDistribution -> Categorical
nameFull name of distribution.
short_nameShort name of distribution for printing.
descriptionBrief description of the distribution.
new()
Creates a new instance of this R6 class.
Categorical$new(elements = NULL, probs = NULL, decorators = NULL)
elementslist()
Categories in the distribution, see examples.
probsnumeric()
Probabilities of respective categories occurring.
decorators(character())
Decorators to add to the distribution during construction.
# Note probabilities are automatically normalised (if not vectorised)
x <- Categorical$new(elements = list("Bapple", "Banana", 2), probs = c(0.2, 0.4, 1))
# Length of elements and probabilities cannot be changed after construction
x$setParameterValue(probs = c(0.1, 0.2, 0.7))
# d/p/q/r
x$pdf(c("Bapple", "Carrot", 1, 2))
x$cdf("Banana") # Assumes ordered in construction
x$quantile(0.42) # Assumes ordered in construction
x$rand(10)
# Statistics
x$mode()
summary(x)
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.
Categorical$mean(...)
...Unused.
mode()
The mode of a probability distribution is the point at which the pdf is a local maximum, a distribution can be unimodal (one maximum) or multimodal (several maxima).
Categorical$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.
Categorical$variance(...)
...Unused.
skewness()
The skewness of a distribution is defined by the third standardised moment,
sk_X = E_X[((x - μ)/σ)^3]
where E_X is the expectation of distribution X, μ is the mean of the distribution and σ is the standard deviation of the distribution.
Categorical$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.
Categorical$kurtosis(excess = TRUE, ...)
excess(logical(1))
If TRUE (default) excess kurtosis returned.
...Unused.
entropy()
The entropy of a (discrete) distribution is defined by
- ∑ (f_X)log(f_X)
where f_X is the pdf of distribution X, with an integration analogue for continuous distributions.
Categorical$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.
Categorical$mgf(t, ...)
t(integer(1))
t integer to evaluate function at.
...Unused.
cf()
The characteristic function is defined by
cf_X(t) = E_X[exp(xti)]
where X is the distribution and E_X is the expectation of the distribution X.
Categorical$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.
Categorical$pgf(z, ...)
z(integer(1))
z integer to evaluate probability generating function at.
...Unused.
setParameterValue()
Sets the value(s) of the given parameter(s).
Categorical$setParameterValue( ..., lst = NULL, error = "warn", resolveConflicts = FALSE )
...ANY
Named arguments of parameters to set values for. See examples.
lst(list(1))
Alternative argument for passing parameters. List names should be parameter names and list values
are the new values to set.
error(character(1))
If "warn" then returns a warning on error, otherwise breaks if "stop".
resolveConflicts(logical(1))
If FALSE (default) throws error if conflicting parameterisations are provided, otherwise
automatically resolves them by removing all conflicting parameters.
clone()
The objects of this class are cloneable with this method.
Categorical$clone(deep = FALSE)
deepWhether to make a deep clone.
McLaughlin, M. P. (2001). A compendium of common probability distributions (pp. 2014-01). Michael P. McLaughlin.
Other discrete distributions:
Bernoulli,
Binomial,
Degenerate,
DiscreteUniform,
EmpiricalMV,
Empirical,
Geometric,
Hypergeometric,
Logarithmic,
Multinomial,
NegativeBinomial,
WeightedDiscrete
Other univariate distributions:
Arcsine,
Bernoulli,
BetaNoncentral,
Beta,
Binomial,
Cauchy,
ChiSquaredNoncentral,
ChiSquared,
Degenerate,
DiscreteUniform,
Empirical,
Erlang,
Exponential,
FDistributionNoncentral,
FDistribution,
Frechet,
Gamma,
Geometric,
Gompertz,
Gumbel,
Hypergeometric,
InverseGamma,
Laplace,
Logarithmic,
Logistic,
Loglogistic,
Lognormal,
NegativeBinomial,
Normal,
Pareto,
Poisson,
Rayleigh,
ShiftedLoglogistic,
StudentTNoncentral,
StudentT,
Triangular,
Uniform,
Wald,
Weibull,
WeightedDiscrete
## ------------------------------------------------
## Method `Categorical$new`
## ------------------------------------------------
# Note probabilities are automatically normalised (if not vectorised)
x <- Categorical$new(elements = list("Bapple", "Banana", 2), probs = c(0.2, 0.4, 1))
# Length of elements and probabilities cannot be changed after construction
x$setParameterValue(probs = c(0.1, 0.2, 0.7))
# d/p/q/r
x$pdf(c("Bapple", "Carrot", 1, 2))
x$cdf("Banana") # Assumes ordered in construction
x$quantile(0.42) # Assumes ordered in construction
x$rand(10)
# Statistics
x$mode()
summary(x)Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.