rmutil (version 1.1.4)

Beta Binomial: Beta Binomial Distribution

Description

These functions provide information about the beta binomial distribution with parameters m and s: density, cumulative distribution, quantiles, and random generation.

The beta binomial distribution with total \(= n\) and prob \(= m\) has density $$p(y) = \frac{B(y+\sigma \mu, n-y+\sigma*(1-\mu)) {n \choose y} }{B(s m,s (1-m))}% $$ for \(y = 0, \ldots, n\) where \(B()\) is the beta function.

Usage

dbetabinom(y, size, m, s, log=FALSE)
pbetabinom(q, size, m, s)
qbetabinom(p, size, m, s)
rbetabinom(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.

See Also

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

Examples

# NOT RUN {
# 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)
pbetabinom(2,10,0.5,1.1)
qbetabinom(0.33,10,0.5,1.1)
rbetabinom(10,10,0.5,1.1)
# }