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)

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.

lower.tail, log.p

Same meaning as in pnorm or qnorm.

Value

dgenray gives the density, pgenray gives the distribution function, qgenray gives the quantile function, and rgenray generates random deviates.

Author

Kai Huang and J. G. Lauder and T. W. Yee

Details

See genrayleigh, 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 Kundu and Raqab (2005).

See also

genrayleigh, rayleigh.

Examples

if (FALSE) { # \dontrun{
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
} # }