explog {VGAM}

The Exponential Logarithmic Distribution

Description

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.

Details

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

Value

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

Note

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

Author(s)

J. G. Lauder and T. W. Yee

See Also

explogff, exponential.

Examples

## Not run: 
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

## End(Not run)