quantile_to_gev | R Documentation |
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.
quantile_to_gev(quant, prob)
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 |
prob |
A numeric vector of length 3. Exceedance probabilities
corresponding to the quantiles in |
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.
A numeric vector of length 3 containing the GEV location, scale and shape parameters.
rprior_quant
for simulation of GEV parameters from
a prior constructed on the quantile scale.
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])
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