R: Double Binomial Distribution

Double Binomial {rmutil} | R Documentation

## Double Binomial Distribution

### Description

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

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

p(y) = c(n,m,s) Choose(n,y) n^(n s) (m/y)^(y s) ((1-m)/(n-y))^(s(n-y)) y^y (n-y)^(n-y)

for y = 0, …, n, where c(.) is a normalizing constant.

### Usage

    ddoublebinom(y, size, m, s, log=FALSE)
    pdoublebinom(q, size, m, s)
    qdoublebinom(p, size, m, s)
    rdoublebinom(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, `dmultbinom` for the multiplicative binomial, and `dbetabinom` for the beta binomial distribution.

### Examples

    # compute P(45 < y < 55) for y double binomial(100,0.5,1.1)
    sum(ddoublebinom(46:54, 100, 0.5, 1.1))
    pdoublebinom(54, 100, 0.5, 1.1)-pdoublebinom(45, 100, 0.5, 1.1)
    pdoublebinom(2,10,0.5,1.1)
    qdoublebinom(0.05,10,0.5,1.1)
    rdoublebinom(10,10,0.5,1.1)

[Package rmutil version 1.1.3 Index]