VGAMdata (version 1.1-13)

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)

Value

doalog gives the density and

poalog gives the distribution function,

qoalog gives the quantile function, and

roalog generates random deviates.

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.

Author

T. W. Yee

Details

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

See Also

Gaitdlog, oalog, oilog, Otlog.

Examples

shape <- 0.75; pobs1 <- 0.10; x <- (-1):7
doalog(x, shape = shape, pobs1 = pobs1)
table(roalog(100, shape = shape, pobs1 = pobs1))

if (FALSE)  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 = ""))