qev: Quantile estimation of a composite extreme value distribution

In evgam: Generalised Additive Extreme Value Models

Quantile estimation of a composite extreme value distribution

Description

Quantile estimation of a composite extreme value distribution

Usage

qev(
  p,
  loc,
  scale,
  shape,
  m = 1,
  alpha = 1,
  theta = 1,
  family,
  tau = 0,
  bgev.args = list(pa = 0.05, pb = 0.2, alpha = 0.5, beta = 0.5),
  start = NULL,
  method = "uniroot"
)

Arguments

p	a scalar giving the quantile of the distribution sought
loc	a scalar, vector or matrix giving the location parameter
scale	as above, but scale parameter
shape	as above, but shape parameter
m	a scalar giving the number of values per return period unit, e.g. 365 for daily data giving annual return levels
alpha	a scalar, vector or matrix of weights if within-block variables not identically distributed and of different frequencies
theta	a scalar, vector or matrix of extremal index values
family	a character string giving the family for which return levels sought
tau	a scalar, vector or matrix of values giving the threshold quantile for the GPD (i.e. 1 - probability of exceedance)
bgev.args	a list specifying parameters of the blended GEV distribution; see Details
start	a 2-vector giving starting values that bound the return level
method	a character string giving the numerical estimation procedure; defaults to "uniroot"

Details

If F is the generalised extreme value, generalised Pareto or blended GEV distribution, qev solves

\prod_{j=1}^n \big\{F_i(z)\}^{m \alpha_j \theta_j} = p.

for i = 1, \ldots, k. So vectors are supplied as $n$-vectors and matrices are supplied as n \times k matrices.

For all distributions, location, scale and shape parameters are given by loc, scale and shape. The generalised Pareto distribution, for \xi \neq 0 and z > u, is parameterised as 1 - (1 - \tau) [1 + \xi (z - u) / \psi_u]^{-1/\xi}, where u, \psi_u and \xi are its location, scale and shape parameters, respectively, and \tau corresponds to argument tau. For the blended GEV distribution pa, pb, alpha and beta specify additional parameters of the blended GEV distribution; see family.evgam for details.

Estimates either use function uniroot or method = "newton" uses the Newton-Rhaphson method. The latter is often much quicker if matrices are supplied, i.e. for k > 1.

Value

A scalar or vector of estimates of p

Examples

qev(0.9, c(1, 2), c(1, 1.1), .1, family = "gev")
qev(0.99, c(1, 2), c(1, 1.1), .1, family = "gpd", tau = 0.9)

# an example representative on monthly estimates at two locations
qev(0.9, matrix(c(1:12, 2:13), 12, 2), 1.1, .1, family = "gev")

# a blended GEV example with default blended GEV specification
qev(0.9, matrix(c(1:12, 2:13), 12, 2), 1.1, .1, family = "bgev")

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