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

`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 1.0 Index]