Zero-Altered Geometric Distribution

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

Usage

dzageom(x, prob, pobs0 = 0, log = FALSE)
pzageom(q, prob, pobs0 = 0)
qzageom(p, prob, pobs0 = 0)
rzageom(n, 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.

prob, log

Parameters from the ordinary geometric distribution (see dgeom).

pobs0

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

Details

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

Value

dzageom gives the density and pzageom gives the distribution function, qzageom gives the quantile function, and rzageom 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

prob <- 0.35; pobs0 <- 0.05; x <- (-1):7
dzageom(x, prob = prob, pobs0 = pobs0)
#> [1] 0.00000000 0.05000000 0.33250000 0.21612500 0.14048125 0.09131281 0.05935333
#> [8] 0.03857966 0.02507678
table(rzageom(100, prob = prob, pobs0 = pobs0))
#> 
#>  0  1  2  3  4  5  6  7 10 
#>  2 32 24 24  5  5  6  1  1 

if (FALSE)  x <- 0:10
barplot(rbind(dzageom(x, prob = prob, pobs0 = pobs0),
                dgeom(x, prob = prob)), las = 1,
        beside = TRUE, col = c("blue", "orange"), cex.main = 0.7,
        ylab = "Probability", names.arg = as.character(x),
        main = paste("ZAG(prob = ", prob, ", pobs0 = ", pobs0,
                   ") [blue] vs",  " Geometric(prob = ", prob,
                   ") [orange] densities", sep = ""))  # \dontrun{}