# hd_add: Add two hyperdirichlet distributions In hyperdirichlet: A Generalization of the Dirichlet Distribution

## Description

Given two hyperdirichlet distributions, “add” them, in the sense of concatenating their information, assumed to be independent.

## Usage

 `1` ```hd_add(e1, e2, assume_validated = FALSE) ```

## Arguments

 `e1,e2` Hyperdirichlet distributions of the same dimension `assume_validated` Boolean, with default `FALSE` meaning that the returned sum cannot be assumed to be proper; so the returned hyperdirichlet object is tested with `is.proper()` (which is time-consuming). Set to `TRUE` only when you know that the sum is proper

## Details

Think of this function as a computerized embodiment of Bayes's theorem with `e1` representing the prior and `e2` representing one or more informative trials.

The basic guts of the function is ```hyperdirichlet(powers(e1) + params(e2))```. Note that this is equivalent to `hyperdirichlet(params(e1) + powers(e2))`.

The functional form is not really intended for the end user; use `e1 + e2` instead (but observe that the sum will be validated using `is.proper()`, which may take a long time).

## Value

Returns a hyperdirichlet distribution

## Author(s)

Robin K. S. Hankin

`hyperdirichlet`,`is.proper`,`Arith`

## Examples

 ```1 2 3 4 5 6 7``` ```dirichlet(1:4) + gd(c(0.1 , 0.3 , 0.5), c(0.2 , 0.4 , 0.9)) uniform(4) + single_bernoulli_obs(4,1,2) data(chess) ch <- as.hyperdirichlet(chess) stopifnot(all(params(ch+ch+ch) == params(ch*3))) ```

hyperdirichlet documentation built on May 31, 2017, 5:18 a.m.