VGAM (version 1.1-12)

Extbetabinom: The Beta-Binomial Distribution

Description

Density, distribution function, quantile function and random generation for the extended beta-binomial distribution.

Usage

dextbetabinom(x, size, prob, rho = 0,
     log = FALSE, forbycol = TRUE)
pextbetabinom(q, size, prob, rho = 0,
     lower.tail = TRUE, forbycol = TRUE)
qextbetabinom(p, size, prob, rho = 0,
     forbycol = TRUE)
rextbetabinom(n, size, prob, rho = 0)

Value

dextbetabinom gives the density,

pextbetabinom gives the distribution function,

qextbetabinom gives the quantile function and

rextbetabinom generates random deviates.

Arguments

x, q

vector of quantiles.

p

vector of probabilities.

size

number of trials.

n

number of observations. Same as runif.

prob

the probability of success \(\mu\). Must be in the unit closed interval \([0,1]\).

rho

the correlation parameter \(\rho\), which may be negative for underdispersion or else be in the interval \([0, 1)\) for overdispersion. The default value of 0 corresponds to the usual binomial distribution with probability prob.

log, lower.tail

Same meaning as runif.

forbycol

Logical. A for loop cycles over either the rows or columns and this argument determines which. The rows are 1:length(x) and the columns are 0:max(size). The best choice is data set dependent.

Warning

Setting rho = 1 is not recommended as NaN is returned, however the code may be modified in the future to handle this special case.

Details

The extended beta-binomial distribution allows for a slightly negative correlation parameter between binary responses within a cluster (e.g., a litter). An exchangeable error structure with correlation \(\rho\) is assumed.

See Also

extbetabinomial, Betabinom, Binomial.

Examples

set.seed(1); rextbetabinom(10, 100, 0.5)
set.seed(1);        rbinom(10, 100, 0.5)  # Same

if (FALSE) N <- 9; xx <- 0:N; prob <- 0.5; rho <- -0.02
dy <- dextbetabinom(xx, N, prob, rho)
barplot(rbind(dy, dbinom(xx, size = N, prob)),
  beside = TRUE, col = c("blue","green"), las = 1,
  main = paste0("Beta-binom(size=", N, 
  ", prob=", prob, ", rho=", rho, ") (blue) vs\n",
  " Binom(size=", N, ", prob=", prob, ") (green)"),
  names.arg = as.character(xx), cex.main = 0.8)
sum(dy * xx)  # Check expected values are equal
sum(dbinom(xx, size = N, prob = prob) * xx)
cumsum(dy) - pextbetabinom(xx, N, prob, rho)  # 0?