VGAM (version 1.1-13)

Zabinom: Zero-Altered Binomial Distribution

Description

Density, distribution function, quantile function and random generation for the zero-altered binomial distribution with parameter pobs0.

Usage

dzabinom(x, size, prob, pobs0 = 0, log = FALSE)
pzabinom(q, size, prob, pobs0 = 0)
qzabinom(p, size, prob, pobs0 = 0)
rzabinom(n, size, prob, pobs0 = 0)

Value

dzabinom gives the density and

pzabinom gives the distribution function,

qzabinom gives the quantile function, and

rzabinom generates random deviates.

Arguments

x, q

vector of quantiles.

p

vector of probabilities.

n

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

size, prob, log

Parameters from the ordinary binomial distribution (see dbinom).

pobs0

Probability of (an observed) zero, called \(pobs0\). The default value of pobs0 = 0 corresponds to the response having a positive binomial distribution.

Author

T. W. Yee

Details

The probability function of \(Y\) is 0 with probability pobs0, else a positive binomial(size, prob) distribution.

See Also

zibinomial, Gaitdbinom.

Examples

size <- 10; prob <- 0.15; pobs0 <- 0.05; x <- (-1):7
dzabinom(x, size = size, prob = prob, pobs0 = pobs0)
table(rzabinom(100, size = size, prob = prob, pobs0 = pobs0))

if (FALSE)  x <- 0:10
barplot(rbind(dzabinom(x, size = size, prob = prob, pobs0 = pobs0),
                dbinom(x, size = size, prob = prob)),
  beside = TRUE, col = c("blue", "orange"), cex.main = 0.7, las = 1,
  ylab = "Probability", names.arg = as.character(x),
  main = paste("ZAB(size = ", size, ", prob = ", prob, ", pobs0 = ", pobs0,
               ") [blue] vs",  " Binom(size = ", size, ", prob = ", prob,
               ") [orange] densities", sep = ""))