dist.Categorical {LaplacesDemon} R Documentation

## 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].

### 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.

### Value

dcat gives the density and rcat generates random deviates.

### Author(s)

Statisticat, LLC. software@bayesian-inference.com

as.indicator.matrix, ddirichlet, and dmultinom.
library(LaplacesDemon)