Beta Binomial {rmutil} R Documentation

## Beta Binomial Distribution

### Description

These functions provide information about the beta binomial distribution with parameters `m` and `s`: density, cumulative distribution, quantiles, and random generation.

The beta binomial distribution with total = n and `prob` = m has density

p(y) = B(y+s m,n-y+s (1-m)) Choose(n,y) / B(s m,s (1-m))

for y = 0, ..., n where B() is the beta function.

### Usage

```dbetabinom(y, size, m, s, log=FALSE)
pbetabinom(q, size, m, s)
qbetabinom(p, size, m, s)
rbetabinom(n, size, m, s)
```

### Arguments

 `y` vector of frequencies `q` vector of quantiles `p` vector of probabilities `n` number of values to generate `size` vector of totals `m` vector of probabilities of success `s` vector of overdispersion parameters `log` if TRUE, log probabilities are supplied.

### Author(s)

J.K. Lindsey

`dbinom` for the binomial, `ddoublebinom` for the double binomial, and `dmultbinom` for the multiplicative binomial distribution.

### Examples

```# compute P(45 < y < 55) for y beta binomial(100,0.5,1.1)
sum(dbetabinom(46:54, 100, 0.5, 1.1))
pbetabinom(54,100,0.5,1.1)-pbetabinom(45,100,0.5,1.1)
pbetabinom(2,10,0.5,1.1)
qbetabinom(0.33,10,0.5,1.1)
rbetabinom(10,10,0.5,1.1)
```

[Package rmutil version 1.0 Index]