BurrXII: Burr Type XII distribution

Description

Provides density, distribution function, quantile function, random value generation, and raw moments of order r for the Burr Type XII distribution.

Usage

dburrXII(x, scale, shape1, shape2, log = FALSE)
pburrXII(q, scale, shape1, shape2, lower.tail = TRUE, log.p = FALSE)
qburrXII(p, scale, shape1, shape2, lower.tail = TRUE, log.p = FALSE)
rburrXII(n, scale, shape1, shape2)
mburrXII(r, scale, shape1, shape2)

Value

dburrXII returns a numeric vector of density values. pburrXII returns a numeric vector of cumulative probabilities. qburrXII returns a numeric vector of quantiles. rburrXII returns a numeric vector of random deviates. mburrXII returns the raw moment of order r.

Arguments

x, q: vector of quantiles.
scale, shape1, shape2: scale and shape parameters; the shape arguments cannot be vectors (must have length one).
log, log.p: logical; if TRUE, probabilities p are given as log(p).
lower.tail: logical; if TRUE (default), probabilities are \(P[X \le x]\), otherwise \(P[X > x]\).
p: vector of probabilities.
n: number of observations. If length(n) > 1, the length is taken to be the number required.
r: raw moment order.

References

Papalexiou, S.M. (2018). Unified theory for stochastic modelling of hydroclimatic processes: Preserving marginal distributions, correlation structures, and intermittency. Advances in Water Resources, 115, 234-252, tools:::Rd_expr_doi("10.1016/j.advwatres.2018.02.013")

Examples

Run this code


## plot the density

ggplot(data.frame(x = c(0, 10)),
       aes(x)) +
  stat_function(fun = dburrXII,
                args = list(scale = 5,
                            shape1 = .25,
                            shape2 = .75),
                colour = "royalblue4") +
  labs(x = "",
       y = "Density") +
  theme_classic()