VGAM (version 1.1-2)

Oalog: One-Altered Logarithmic Distribution

Description

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

Usage

doalog(x, shape, pobs1 = 0, log = FALSE)
poalog(q, shape, pobs1 = 0)
qoalog(p, shape, pobs1 = 0)
roalog(n, shape, pobs1 = 0)

Arguments

x, q, n, p

Same Unif.

shape, log

Same as Otlog).

pobs1

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

Value

doalog gives the density and poalog gives the distribution function, qoalog gives the quantile function, and roalog generates random deviates.

Details

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

See Also

oalog, oilog, Otlog.

Examples

# NOT RUN {
shape <- 0.75; pobs1 <- 0.10; x <- (-1):7
doalog(x, shape = shape, pobs1 = pobs1)
table(roalog(100, shape = shape, pobs1 = pobs1))

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