VGAM (version 1.1-2)

Oazeta: One-Altered Logarithmic Distribution

Description

Density, distribution function, quantile function and random generation for the one-altered zeta distribution with parameter pobs1.

Usage

doazeta(x, shape, pobs1 = 0, log = FALSE)
poazeta(q, shape, pobs1 = 0)
qoazeta(p, shape, pobs1 = 0)
roazeta(n, shape, pobs1 = 0)

Arguments

x, q, n, p

Same Unif.

shape, log

Same as Otzeta).

pobs1

Probability of (an observed) one, called \(pobs1\). The default value of pobs1 = 0 corresponds to the response having a 1-truncated zeta distribution.

Value

doazeta gives the density and poazeta gives the distribution function, qoazeta gives the quantile function, and roazeta generates random deviates.

Details

The probability function of \(Y\) is 1 with probability pobs1, else a 1-truncated zeta distribution.

See Also

oazeta, Oizeta, Otzeta, zeta.

Examples

# NOT RUN {
shape <- 1.1; pobs1 <- 0.10; x <- (-1):7
doazeta(x, shape = shape, pobs1 = pobs1)
table(roazeta(100, shape = shape, pobs1 = pobs1))

# }
# NOT RUN {
 x <- 0:10
barplot(rbind(doazeta(x, shape = shape, pobs1 = pobs1),
                dzeta(x, shape = shape)),
        beside = TRUE, col = c("blue", "orange"), cex.main = 0.7, las = 1,
        ylab = "Probability", names.arg = as.character(x),
        main = paste("OAZ(shape = ", shape, ", pobs1 = ", pobs1,
                   ") [blue] vs",  " zeta(shape = ", shape,
                   ") [orange] densities", sep = "")) 
# }