hint (version 0.1-3)

Binomialintersection: The Binomial Intersection Distribution

Description

Density, distribution function, quantile function and random generation for the binomial intersection distribution.

Usage

dbint(n, A, range = NULL, log = FALSE)
pbint(n, A, vals, upper.tail = TRUE, log.p = FALSE)
qbint(p, n, A, upper.tail = TRUE, log.p = FALSE)
rbint(num = 5, n, A)

Arguments

n

An integer specifying the number of categories in the urns.

A

A vector of integers specifying the numbers of balls drawn from each urn. The length of the vector equals the number of urns.

range

A vector of integers specifying the intersection sizes for which probabilities (dhint) or cumulative probabilites (phint) should be computed (can be a single number). If range is NULL (default) then probabilities will be returned over the entire range of possible values.

log

Logical. If TRUE, probabilities p are given as log(p). Defaults to FALSE.

vals

A vector of integers specifying the intersection sizes for which probabilities (dhint) or cumulative probabilites (phint) should be computed (can be a single number). If range is NULL (default) then probabilities will be returned over the entire range of possible values.

upper.tail

Logical. If TRUE, probabilities are P(X >= v), else P(X <= v). Defaults to TRUE.

log.p

Logical. If TRUE, probabilities p are given as log(p). Defaults to FALSE.

p

A probability between 0 and 1.

num

An integer specifying the number of random numbers to generate. Defaults to 5.

Details

The binomial intersection distribution is given by $$ P(X = v|N) = {b \choose v} \left(\prod_{i=1}^{N-1} p_{i}\right)^{v} \left(1 - \prod_{i=1}^{N-1} p_{i}\right)^{b-v} $$ where b gives the sample size which is smallest. This is an approximation for the hypergeometric intersection distribution when \(n\) is large and \(b\) is small relative to the samples taken from the \(N-1\) other urns.

Examples

# NOT RUN {
## Generate the distribution of intersections sizes:
dd <- dbint(20, c(10, 12, 11, 14))
## Restrict the range of intersections.
dd <- dbint(20, c(10, 12), range = 0:5)
## Generate cumulative probabilities.
pp <- pbint(29, c(15, 8), vals = 5)
pp <- pbint(29, c(15, 8), vals = 2, upper.tail = FALSE)
## Extract quantiles:
qq <- qbint(0.15, 23, c(12, 10))
## Generate random samples from Binomial intersection distributions.
rr <- rbint(num = 10, 18, c(9, 14))
# }