Computation of posterior quantiles for an extreme value mixture model
quant(x, ...)# S3 method for evmm
quant(x, values = NULL, cred = 0.95, ...)
A list with the following entries:
quantiles: a matrix containing the quantiles, the posterior credibility intervals and the empirical estimate.
data: the dataset used to estimate the quantiles.
complete: a matrix with the quantiles for each value in the posterior sample.
the output of a model estimated with extrememix.
additional arguments for compatibility.
numeric vector of values of which to compute the quantile.
amplitude of the posterior credibility interval.
For a random variable \(X\) the p-quantile is the value \(x\) such that \(P(X>x)=1-p\). For an extreme value mixture model this can be computed as $$x = u +\frac{\sigma}{\xi}((1-p^*)^{-\xi}-1),$$ where $$p^* = \frac{p-F_\textnormal{bulk}(u|\theta)}{1-F_\textnormal{bulk}(u|\theta)},$$ and \(F_\textnormal{bulk}\) is the distribution function of the bulk, parametrized by \(\theta\).
do Nascimento, Fernando Ferraz, Dani Gamerman, and Hedibert Freitas Lopes. "A semiparametric Bayesian approach to extreme value estimation." Statistics and Computing 22.2 (2012): 661-675.