VGAMdata (version 1.1-13)

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)

Value

doazeta gives the density and

poazeta gives the distribution function,

qoazeta gives the quantile function, and

roazeta generates random deviates.

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.

Author

T. W. Yee

Details

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

See Also

oazeta, Oizeta, Otzeta, zeta.

Examples

shape <- 1.1; pobs1 <- 0.10; x <- (-1):7
doazeta(x, shape = shape, pobs1 = pobs1)
table(roazeta(100, shape = shape, pobs1 = pobs1))

if (FALSE)  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 = ""))