The Multiplicative Binomial Distribution

Usage

dmultbinom(y, n, m, s)
pmultbinom(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 multiplicative binomial distribution with parameters m and s. dmultbinom gives the density and pmultbinom gives the distribution function.

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

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

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

Author(s)

J.K. Lindsey

See Also

dbinom for the binomial, ddoublebinom for the double binomial, and dbetabinom for the beta binomial distribution.

Examples

# Compute P(45 < y < 55) for y multiplicative binomial(100,0.5,1.1)
sum(dmultbinom(46:54, 100, 0.5, 1.1))
pmultbinom(54, 100, 0.5, 1.1)-pmultbinom(45, 100, 0.5, 1.1)


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