qev function

Quantile estimation of a composite extreme value distribution

qev(
  p,
  loc,
  scale,
  shape,
  m = 1,
  alpha = 1,
  theta = 1,
  family,
  tau = 0,
  start = NULL
)

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

Returns

A scalar or vector of estimates of p

Details

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

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)