Double Binomial Distribution
These functions provide information about the double binomial
distribution with parameters m and s: density,
cumulative distribution, quantiles, and random generation.
The double binomial distribution with total = n and
prob = m has density
p(y) = c(n,m,s) Choose(n,y) n^(n s) (m/y)^(y s) ((1-m)/(n-y))^(s(n-y)) y^y (n-y)^(n-y)
for y = 0, …, n, where c(.) is a normalizing constant.
ddoublebinom(y, size, m, s, log=FALSE) pdoublebinom(q, size, m, s) qdoublebinom(p, size, m, s) rdoublebinom(n, size, m, s)
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. |
J.K. Lindsey
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) pdoublebinom(2,10,0.5,1.1) qdoublebinom(0.05,10,0.5,1.1) rdoublebinom(10,10,0.5,1.1)
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