ddoublebinom(y, n, m, s) pdoublebinom(q, n, m, s)
y
| vector of frequencies |
q
| vector of quantiles |
n
| vector of totals |
m
| vector of probabilities |
s
| vector of overdispersion 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.dbinom
for the binomial, dmultbinom
for
the multiplicative binomial, and dbetabinom
for the beta binomial distribution.# 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)