# DoubleBinom: Double Binomial Distribution In rmutil: Utilities for Nonlinear Regression and Repeated Measurements Models

## 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

 ```1 2 3 4``` ```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

`dbinom` for the binomial, `dmultbinom` for the multiplicative binomial, and `dbetabinom` for the beta binomial distribution.
 ```1 2 3 4 5 6``` ```# 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) ```