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 |

`n` |
This is the number of observations, which must be a positive
integer that has length 1. When |

`p` |
This is a vector of length |

`pr` |
This is a vector of probabilities, or log-probabilities. |

`log` |
Logical. If |

`log.pr` |
Logical. if |

`lower.tail` |
Logical. if |

### 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)`

= UnknownVariance:

`var(\theta)`

= UnknownMode:

`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))
```

*LaplacesDemon*version 16.1.6 Index]