R: Multiplicative Binomial Distribution

Multiplicative Binomial {rmutil} | R Documentation

## Multiplicative Binomial Distribution

### Description

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

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

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

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

### Usage

    dmultbinom(y, size, m, s, log=FALSE)
    pmultbinom(q, size, m, s)
    qmultbinom(p, size, m, s)
    rmultbinom(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 `dbetabinom` for the beta binomial distribution.

### Examples

    # compute P(45 < y < 55) for y multiplicative binomial(100,0.5,1.1)
    sum(dmultbinom(46:54, 100, 0.5, 1.1))
    pmultbinom(54, 100, 0.5, 1.1)-pmultbinom(45, 100, 0.5, 1.1)
    pmultbinom(2,10,0.5,1.1)
    qmultbinom(0.025,10,0.5,1.1)
    rmultbinom(10,10,0.5,1.1)

[Package rmutil version 1.1.3 Index]