The Exponential Logarithmic Distribution

Density, distribution function, quantile function and random generation for the exponential logarithmic distribution.

Usage

dexplog(x, scale = 1, shape, log = FALSE)
pexplog(q, scale = 1, shape)
qexplog(p, scale = 1, shape) 
rexplog(n, scale = 1, shape)

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.

scale, shape

positive scale and shape parameters.

log

Logical. If log = TRUE then the logarithm of the density is returned.

Value

dexplog gives the density, pexplog gives the distribution function, qexplog gives the quantile function, and rexplog generates random deviates.

Author

J. G. Lauder and T. W. Yee

Details

See explogff, the VGAM family function for estimating the parameters, for the formula of the probability density function and other details.

Note

We define scale as the reciprocal of the scale parameter used by Tahmasabi and Rezaei (2008).

See also

explogff, exponential.

Examples

if (FALSE) { # \dontrun{
shape <- 0.5; scale <- 2; nn <- 501
x <- seq(-0.50, 6.0, len = nn)
plot(x, dexplog(x, scale, shape), type = "l", las = 1, ylim = c(0, 1.1),
     ylab = paste("[dp]explog(shape = ", shape, ", scale = ", scale, ")"),
     col = "blue", cex.main = 0.8,
     main = "Blue is density, orange is cumulative distribution function",
     sub = "Purple lines are the 10,20,...,90 percentiles")
lines(x, pexplog(x, scale, shape), col = "orange")
probs <- seq(0.1, 0.9, by = 0.1)
Q <- qexplog(probs, scale, shape = shape)
lines(Q, dexplog(Q, scale, shape = shape), col = "purple", lty = 3, type = "h")
lines(Q, pexplog(Q, scale, shape = shape), col = "purple", lty = 3, type = "h")
abline(h = probs, col = "purple", lty = 3)
max(abs(pexplog(Q, scale, shape = shape) - probs)) # Should be 0
} # }