evgam (version 1.0.1)

qev: 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,
  start = NULL
)

Value

A scalar or vector of estimates of p

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)

start

a 2-vector giving starting values that bound the return level

Details

If \(F\) is the generalised extreme value or generalised Pareto distribution, qev solves $$\prod_{j=1}^n \big\{F(z)\}^{m \alpha_j \theta_j} = p.$$

For both 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.

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)