R: Categorical Distribution

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 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. software@bayesian-inference.com

### See Also

`as.indicator.matrix`, `ddirichlet`, and `dmultinom`.

### Examples

    library(LaplacesDemon)
    dcat(x=1, p=c(0.3,0.3,0.4))
    rcat(n=10, p=c(0.1,0.3,0.6))

[Package LaplacesDemon version 16.1.1 Index]