The Beta Binomial Distribution

Usage

dbetabinom(y, n, m, s)
pbetabinom(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 beta binomial distribution with parameters m and s. dbetabinom gives the density and pbetabinom gives the distribution function.

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

p(y) = B(y+s m,n-y+s (1-m)) Choose(n,y) / B(s m,s (1-m))

for y = 0, ..., n where B() is the beta function.

Author(s)

J.K. Lindsey

See Also

dbinom for the binomial, ddoublebinom for the double binomial, and dmultbinom for the multiplicative binomial distribution.

Examples

# Compute P(45 < y < 55) for y beta binomial(100,0.5,1.1)
sum(dbetabinom(46:54, 100, 0.5, 1.1))
pbetabinom(54,100,0.5,1.1)-pbetabinom(45,100,0.5,1.1)


[Package Contents]