Double Binomial {rmutil}R Documentation

The Double Binomial Distribution

Usage

ddoublebinom(y, n, m, s)
pdoublebinom(q, n, m, s)

Arguments

y vector of frequencies
q vector of quantiles
n vector of totals
m vector of probabilities
s vector of overdispersion parameters

Value

These functions provide information about the double binomial distribution with parameters m and s. ddoublebinom gives the density and pdoublebinom gives the distribution function.

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

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

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

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)


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