# Rev Language Reference

## dnCategorical - The Categorical Distribution

The categorical distribution, sometimes referred to as the generalized Bernoulli distribution. It describes the probability of one of K different outcomes, labeled from 1 to K, with each outcome probability separately specified.

• dnCat

### Usage

dnCategorical(Simplex p)

### Arguments

 p : Simplex (pass by const reference) The probability for each category.

### Details

The argument to the constructor is a simplex containing the probabilities of the outcomes. The outcomes are labeled from 1 to K, where K is the number of elements in the simplex. Outcome i has probability specified by component i in the simplex. A typical scenario where a categorical variable is used is in the definition of a variable drawn from a mixture. A vector of mixture components is set up first, and then a stochastic variable drawn from a categorical distribution is used as an index in a deterministic assignment that points to a component in the mixture. See example below.

### Example

# Define a stochastic variable x that is drawn from
# a categorical distribution with 4 categories, each
# category having the same probability, then examine
# the value of x.
x ~ dnCat( simplex(1,1,1,1) )
x

# Draw 10 values from the distribution and place them
# in a vector a, then examine a.
for ( i in 1:10 ) {
a[i] <- x
x.redraw()
}
a

# Use x in defining a deterministic variable y taking
# on values from a mixture of RealPos values representing
# rates from a discretized scaled gamma distribution
# with four categories.
shape ~ dnExp( 10.0 )
rates := fnDiscretizeGamma( shape, shape, 4 )
y := rates[x]