LaplacesDemon (version 16.1.0)

dist.Categorical: Categorical Distribution

Description

This is the density and random deviates function for the categorical distribution with probabilities parameter \(p\).

Usage

dcat(x, p, log=FALSE)
qcat(pr, p, lower.tail=TRUE, log.pr=FALSE)
rcat(n, p)

Arguments

x

This is a vector of discrete data with \(k\) discrete categories, and is of length \(n\). This function also accepts \(x\) after it has been converted to an \(n \times k\) indicator matrix, such as with the as.indicator.matrix function.

n

This is the number of observations, which must be a positive integer that has length 1. When p is supplied to rcat as a matrix, n must equal the number of rows in p.

p

This is a vector of length \(k\) or \(n \times k\) matrix of probabilities. The qcat function requires a vector.

pr

This is a vector of probabilities, or log-probabilities.

log

Logical. If log=TRUE, then the logarithm of the density is returned.

log.pr

Logical. if TRUE, probabilities \(pr\) are given as \(\log(pr)\).

lower.tail

Logical. if TRUE (default), probabilities are \(Pr[X \le x]\), otherwise, \(Pr[X > x]\).

Value

dcat gives the density and rcat generates random deviates.

Details

• Application: Discrete Univariate

• Density: \(p(\theta) = \sum \theta p\)

• Inventor: Unknown (to me, anyway)

• Notation 1: \(\theta \sim \mathcal{CAT}(p)\)

• Notation 2: \(p(\theta) = \mathcal{CAT}(\theta | p)\)

• Parameter 1: probabilities \(p\)

• Mean: \(E(\theta)\) = Unknown

• Variance: \(var(\theta)\) = Unknown

• Mode: \(mode(\theta)\) = Unknown

Also called the discrete distribution, the categorical distribution describes the result of a random event that can take on one of \(k\) possible outcomes, with the probability \(p\) of each outcome separately specified. The vector \(p\) of probabilities for each event must sum to 1. The categorical distribution is often used, for example, in the multinomial logit model. The conjugate prior is the Dirichlet distribution.

See Also

as.indicator.matrix, ddirichlet, and dmultinom.

Examples

# NOT RUN {
library(LaplacesDemon)
dcat(x=1, p=c(0.3,0.3,0.4))
rcat(n=10, p=c(0.1,0.3,0.6))
# }