quant: Estimated Quantiles

In manueleleonelli/extrememix: Bayesian Estimation of Extreme Value Mixture Models

Estimated Quantiles

Description

Computation of posterior quantiles for an extreme value mixture model

Usage

quant(x, ...)

## S3 method for class 'evmm'
quant(x, values = NULL, cred = 0.95, ...)

Arguments

x	the output of a model estimated with extrememix.
...	additional arguments for compatibility.
values	numeric vector of values of which to compute the quantile.
cred	amplitude of the posterior credibility interval.

Details

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.

Value

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.

References

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.

Examples

quant(rainfall_ggpd)

manueleleonelli/extrememix documentation built on Oct. 25, 2024, 6:24 p.m.