Zero-Altered Binomial Distribution

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)

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.

Details

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

Value

dzabinom gives the density and pzabinom gives the distribution function, qzabinom gives the quantile function, and rzabinom generates random deviates.

Author

T. W. Yee

Note

The argument pobs0 is recycled to the required length, and must have values which lie in the interval \([0,1]\).

Examples

size <- 10; prob <- 0.15; pobs0 <- 0.05; x <- (-1):7
dzabinom(x, size = size, prob = prob, pobs0 = pobs0)
#> [1] 0.0000000000 0.0500000000 0.4109620590 0.3263522233 0.1535775169
#> [6] 0.0474283508 0.0100436508 0.0014770075 0.0001489419
table(rzabinom(100, size = size, prob = prob, pobs0 = pobs0))
#> 
#>  0  1  2  3  4 
#>  7 38 36 15  4 

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 = ""))  # \dontrun{}