Converts quantiles to GEV parameters

Three quantiles, that is, the value of quantile and their respective exceedance probabilities, are provided. This function attempts to find the location, scale and shape parameters of a GEV distribution that has these quantiles.

Usage

quantile_to_gev(quant, prob)

Arguments

quant

A numeric vector of length 3. Values of the quantiles. The values should increase with the index of the vector. If not, the values in quant will be sorted into increasing order without warning.

prob

A numeric vector of length 3. Exceedance probabilities corresponding to the quantiles in quant. The values should decrease with the index of the vector. If not, the values in prob will be sorted into decreasing order without warning.

Value

A numeric vector of length 3 containing the GEV location, scale and shape parameters.

Details

Suppose that \(G(x)\) is the distribution function of a GEV(\(\mu, \sigma, \xi\)) distribution. This function attempts to solve numerically the set of three non-linear equations $$G(q_i) = 1 - p_i, i = 1, 2, 3$$ where \(q_i, i=1,2,3\) are the quantiles in quant and \(p_i, i=1,2,3\) are the exceedance probabilities in prob. This is reduced to a one-dimensional optimisation over the GEV shape parameter.

See also

rprior_quant for simulation of GEV parameters from a prior constructed on the quantile scale.

Examples

my_q <- c(15, 20, 22.5)
my_p <- 1-c(0.5, 0.9, 0.5^0.01)
x <- quantile_to_gev(quant = my_q, prob = my_p)
# Check
qgev(p = 1 - my_p, loc = x[1], scale = x[2], shape = x[3])
#> [1] 15.0 20.0 22.5