Informative GEV prior on a quantile scale

Informative GEV prior for GEV parameters (\(\mu, \sigma, \xi\)) constructed on the quantile scale. For information about how to set this prior see set_prior.

Usage

gev_quant(pars, prob, shape, scale, min_xi = -Inf, max_xi = Inf, trendsd = 0)

Arguments

pars

A numeric vector of length 3. GEV parameters (\(\mu, \sigma, \xi\)).

prob

A numeric vector of length 3 containing exceedance probabilities (\(p_1, p_2, p_3\)) such that \(p_1 > p_2 > p_3\). If the values in quant are not ordered from largest to smallest then they will be ordered inside set_prior without warning.

shape, scale

Numeric vectors of length 3. Shape and scale parameters specifying (independent) gamma prior distributions placed on the differences between the quantiles corresponding to the probabilities given in prob.

min_xi

A numeric scalar. Prior lower bound on \(\xi\).

max_xi

A numeric scalar. Prior upper bound on \(\xi\).

trendsd

Has no function other than to achieve compatibility with function in the evdbayes package.

Value

The log of the prior density.

Details

See Coles and Tawn (1996) and/or Stephenson (2016) for details.

Note that the lower end point of the distribution of the distribution of the variable in question is assumed to be equal to zero. If this is not the case then the user should shift the data to ensure that this is true.

References

Coles, S. G. and Tawn, J. A. (1996) A Bayesian analysis of extreme rainfall data. Appl. Statist., 45, 463-478.

Stephenson, A. (2016) Bayesian inference for extreme value modelling. In Extreme Value Modeling and Risk Analysis: Methods and Applications (eds D. K. Dey and J. Yan), 257-280, Chapman and Hall, London. doi:10.1201/b19721 .