extraDistr (version 1.8.1)

BetaBinom: Beta-binomial distribution

Description

Probability mass function and random generation for the beta-binomial distribution.

Usage

dbbinom(x, size, alpha = 1, beta = 1, log = FALSE)
pbbinom(q, size, alpha = 1, beta = 1, lower.tail = TRUE, log.p = FALSE)
rbbinom(n, size, alpha = 1, beta = 1)

Arguments

x, q

vector of quantiles.

size

number of trials (zero or more).

alpha, beta

non-negative parameters of the beta distribution.

log, log.p

logical; if TRUE, probabilities p are given as log(p).

lower.tail

logical; if TRUE (default), probabilities are $P[X \le x]$ otherwise, $P[X > x]$.

n

number of observations. If length(n) > 1, the length is taken to be the number required.

Details

If $p ~ Beta(\alpha, \beta)$ and $X ~ Binomial(n, p)$, then $X ~ BetaBinomial(n, \alpha, \beta)$.

Probability mass function $$ f(x) = {n \choose x} \frac{\mathrm{B}(x+\alpha, n-x+\beta)}{\mathrm{B}(\alpha, \beta)} $$

Warning: cumulative distribution function is defined as $$F(x) = \sum_{k=0}^x f(k)$$ so it may be slow for large datasets.

See Also

Beta, Binomial

Examples

x <- rbbinom(1e5, 1000, 5, 13)
xx <- 0:1000
hist(x, 100, freq = FALSE)
lines(xx-0.5, dbbinom(xx, 1000, 5, 13), col = "red")
hist(pbbinom(x, 1000, 5, 13))
plot(ecdf(x))
lines(xx, pbbinom(xx, 1000, 5, 13), col = "red", lwd = 2)