bgev: The blended generalised extreme value distribution

In evgam: Generalised Additive Extreme Value Models

The blended generalised extreme value distribution

Description

Density, distribution function, quantile function and random generation for the blended generalised extreme value distribution with parameters location, scale, shape, pa, pb, alpha and beta.

Usage

dbgev(
  x,
  location,
  scale,
  shape,
  pa = 0.05,
  pb = 0.2,
  alpha = 0.5,
  beta = 0.5,
  log = FALSE
)

pbgev(
  q,
  location,
  scale,
  shape,
  pa = 0.05,
  pb = 0.2,
  alpha = 0.5,
  beta = 0.5,
  lower.tail = TRUE,
  log.p = FALSE
)

qbgev(
  p,
  location,
  scale,
  shape,
  pa = 0.05,
  pb = 0.2,
  alpha = 0.5,
  beta = 0.5,
  lower.tail = TRUE,
  log.p = FALSE
)

rbgev(n, location, scale, shape, pa = 0.05, pb = 0.2, alpha = 0.5, beta = 0.5)

Arguments

x, q	vector of quantiles.
location, scale, shape	location, scale and shape parameters.
pa, pb, alpha, beta	Gumbel to GEV mixing parameters; see Details.
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.

Details

The blended generalised extreme value distribution with location parameter q_\alpha, scale parameter s_\beta and shape parameter \xi has cumulative distribution function given by

H(x \mid q_\alpha, s_\beta, \xi) = F(x \mid q_\alpha, s_\beta, \xi)^{p(x')} G(x \mid \tilde q_\alpha \tilde s_\beta)^{1 - p(x')}

where

F(x \mid q_\alpha, s_\beta, \xi) = \exp \left\{ - \left[ \dfrac{x - q_\alpha}{s_\beta(\ell_{1 - \beta / 2, \xi} - \ell_{\beta / 2, \xi})^{-1}} + \ell_{\alpha, \xi} \right]^{-1/\xi}_+ \right\}

with \ell_{a, \xi} = (-\log a)^{-\xi}, [x]_+ = \max(0, x), alpha and beta parameters \alpha and \beta, respectively,

G(x \mid q_{\tilde \alpha}, s_{\tilde \beta}) = \exp\left\{ -\exp\left[- \left\{\dfrac{x - \tilde q_\alpha}{\tilde s_\beta(\ell_{1 - \beta / 2} - \ell_{\beta / 2})^{-1}} + \ell_{\alpha} \right\}\right]\right\}

with \ell_a = \log(-\log a),

\tilde q_\alpha = a - \dfrac{(b - a)(\ell_\alpha - \ell_{p_a}))}{\ell_{p_a} - \ell_{p_b}}~~\text{and}~~\tilde s_\beta = \dfrac{(b - a)(\ell_{\beta / 2} - \ell_{1 - \beta/2})}{\ell_{p_a} - \ell_{p_b}},

with a = F^{-1}(p_a \mid q_\alpha, s_\beta, \xi), b = F^{-1}(p_b \mid q_\alpha, s_\beta, \xi), with pa and pb parameters p_a and p_b, respectively, and where x' = (x - a) / (b - a) and p(x) denotes the cumulative distribution of the Beta(5, 5) distribution.

Default values for pa, pb, alpha and beta are taken from Castro-Camilo et al. (2022).

Value

dbgev gives the density, pbgev gives the distribution function, qbgev gives the quantile function, and rbgev generates random deviates.

References

Castro-Camilo, D., Huser, R., & Rue, H. (2022). Practical strategies for generalized extreme value-based regression models for extremes. Environmetrics, 33(6), e2742. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1002/env.2742")}

See Also

predict.evgam

Examples

dbgev(3, 2, 1, .1)

evgam documentation built on Sept. 3, 2026, 5:09 p.m.