The Exponential Logarithmic Distribution
Density, distribution function, quantile function and random generation for the exponential logarithmic distribution.
dexplog(x, scale = 1, shape, log = FALSE) pexplog(q, scale = 1, shape) qexplog(p, scale = 1, shape) rexplog(n, scale = 1, shape)
x, q |
vector of quantiles. |
p |
vector of probabilities. |
n |
number of observations.
If |
scale, shape |
positive scale and shape parameters. |
log |
Logical.
If |
See explogff, the VGAM family function
for estimating the parameters,
for the formula of the probability density function and other details.
dexplog gives the density,
pexplog gives the distribution function,
qexplog gives the quantile function, and
rexplog generates random deviates.
We define scale as the reciprocal of the scale parameter
used by Tahmasabi and Rezaei (2008).
J. G. Lauder and T. W. Yee
## 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
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