# dbetabinom: Beta-binomial probability density In joepowers16/rethinking: Statistical Rethinking book package

## Description

Functions for computing density and producing random samples from a beta-binomial probability distribution.

## Usage

 ```1 2``` ```dbetabinom( x , size , prob , theta , shape1 , shape2 , log=FALSE ) rbetabinom( n , size , prob , theta , shape1 , shape2 ) ```

## Arguments

 `x` Integer values to compute probabilies of `size` Number of trials `prob` Average probability of beta distribution `theta` Dispersion of beta distribution `shape1` First shape parameter of beta distribution (alpha) `shape2` Second shape parameter of beta distribution (beta) `log` If `TRUE`, returns log-probability instead of probability `n` Number of random observations to sample

## Details

These functions provide density and random number calculations for beta-binomial observations. The `dbetabinom` code is based on Ben Bolker's original code in the `emdbook` package.

Either `prob` and `theta` OR `shape1` and `shape2` must be provided. The two parameterizations are related by shape1 = prob * theta, shape2 = (1-prob) * theta.

The `rbetabinom` function generates random beta-binomial observations by using both `rbeta` and `rbinom`. It draws `n` values from a beta distribution. Then for each, it generates a random binomial observation.

## Author(s)

Richard McElreath

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30``` ```## Not run: data(reedfrogs) reedfrogs\$pred_yes <- ifelse( reedfrogs\$pred=="pred" , 1 , 0 ) # map model fit # note exp(log_theta) to constrain theta to positive reals m <- map( alist( surv ~ dbetabinom( density , p , exp(log_theta) ), logit(p) <- a + b*pred_yes, a ~ dnorm(0,10), b ~ dnorm(0,1), log_theta ~ dnorm(1,10) ), data=reedfrogs ) # map2stan model fit # constraint on theta is passed via contraints list m.stan <- map2stan( alist( surv ~ dbetabinom( density , p , theta ), logit(p) <- a + b*pred_yes, a ~ dnorm(0,10), b ~ dnorm(0,1), theta ~ dcauchy(0,1) ), data=reedfrogs, constraints=list(theta="lower=0") ) ## End(Not run) ```

joepowers16/rethinking documentation built on June 2, 2019, 6:52 p.m.