rmutil (version 1.1.10)

Double Binomial: 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 $$p(y) = c({n}, {m}, {s}){n \choose y} {n}^{{n}{s}} ({m}/{y})^({y}{s}) {((1-m)/(n-y))}^(({n-y})s y) {y}^{y} {(n-y)}^{(n-y)})% $$ for \(y = 0, \ldots, n\), 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

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)