dBetaBinom: A beta binomial distribution and beta function for use in...
In nimble-dev/nimbleEcology: Distributions for Ecological Models in 'nimble'

Description Usage Arguments Details Author(s) See Also Examples

dBetaBinom and dBetaBinom_One provide a beta binomial distribution that can be used directly from R or in nimble models. These are also used by beta binomial variations of dNmixture distributions. nimBetaFun is the beta function.

nimBetaFun(a, b, log)

dBetaBinom(x, N, shape1, shape2, log = 0)

dBetaBinom_One(x, N, shape1, shape2, log = 0)

rBetaBinom(n, N, shape1, shape2)

rBetaBinom_One(n, N, shape1, shape2)

`a`	shape1 argument of the beta function nimBetaFun.
`b`	shape2 argument of the beta function nimBetaFun.
`log`	TRUE or 1 to return log probability. FALSE or 0 to return probability.
`x`	vector of integer counts.
`N`	number of trials, sometimes called "size".
`shape1`	shape1 parameter of the beta-binomial distribution.
`shape2`	shape2 parameter of the beta-binomial distribution.
`n`	number of random draws, each returning a vector of length `len`. Currently only `n = 1` is supported, but the argument exists for standardization of "`r`" functions.

These nimbleFunctions provide distributions that can be used directly in R or in nimble hierarchical models (via nimbleCode and nimbleModel). They were originally written for the beta binomial N-mixture extensions.

The beta binomial distribution is equivalent to a binomial distribution whose probability is itself a beta distributed random variable.

The probability mass function of the beta binomial is choose(N, x) * B(x + shape1, N - x + shape2) / B(shape1, shape2), where B(shape1, shape2) is the beta function.

The beta binomial distribution is provided in two forms. dBetaBinom and rBetaBinom are used when x is a vector (i.e. length(x) > 1), in which case the parameters alpha and beta must also be vectors. When x is scalar, dBetaBinom_One and rBetaBinom_One are used.

Ben Goldstein and Perry de Valpine

For beta binomial N-mixture models, see dNmixture. For documentation on the beta function, use ?stats::dbeta

# Calculate a beta binomial probability
dBetaBinom(x = c(4, 0, 0, 3), N = 10,
  shape1 = c(0.5, 0.5, 0.3, 0.5), shape2 = c(0.2, 0.4, 1, 1.2))
# Same for case with one observation
dBetaBinom_One(x = 3, N = 10, shape1 = 0.5, shape2 = 0.5, log = TRUE)