R: Beta Binomial Distribution

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

### See Also

`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 1.1.3 Index]