# dist.Categorical: Categorical Distribution In LaplacesDemon: Complete Environment for Bayesian Inference

## Description

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

## Usage

 ```1 2 3``` ```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 x 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 x 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 <= x], otherwise, Pr[X > x].

## Details

• Application: Discrete Univariate

• Density: p(theta) = Sum (theta * p)

• Inventor: Unknown (to me, anyway)

• Notation 1: theta ~ CAT(p)

• Notation 2: p(theta) = 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. [email protected]

`as.indicator.matrix`, `ddirichlet`, and `dmultinom`.
 ```1 2 3``` ```library(LaplacesDemon) dcat(x=1, p=c(0.3,0.3,0.4)) rcat(n=10, p=c(0.1,0.3,0.6)) ```