The Generalized Rayleigh Distribution
Density, distribution function, quantile function and random generation for the generalized Rayleigh distribution.
dgenray(x, scale = 1, shape, log = FALSE) pgenray(q, scale = 1, shape, lower.tail = TRUE, log.p = FALSE) qgenray(p, scale = 1, shape, lower.tail = TRUE, log.p = FALSE) rgenray(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 |
lower.tail, log.p |
See genrayleigh, the VGAM family function
for estimating the parameters,
for the formula of the probability density function and other details.
dgenray gives the density,
pgenray gives the distribution function,
qgenray gives the quantile function, and
rgenray generates random deviates.
We define scale as the reciprocal of the scale parameter
used by Kundu and Raqab (2005).
Kai Huang and J. G. Lauder and T. W. Yee
## Not run:
shape <- 0.5; Scale <- 1; nn <- 501
x <- seq(-0.10, 3.0, len = nn)
plot(x, dgenray(x, shape, scale = Scale), type = "l", las = 1, ylim = c(0, 1.2),
ylab = paste("[dp]genray(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, pgenray(x, shape, scale = Scale), col = "orange")
probs <- seq(0.1, 0.9, by = 0.1)
Q <- qgenray(probs, shape, scale = Scale)
lines(Q, dgenray(Q, shape, scale = Scale), col = "purple", lty = 3, type = "h")
lines(Q, pgenray(Q, shape, scale = Scale), col = "purple", lty = 3, type = "h")
abline(h = probs, col = "purple", lty = 3)
max(abs(pgenray(Q, shape, scale = Scale) - probs)) # Should be 0
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