[R] lmom and lmomRFA Upper and Lower Bounds Simulation Questions

[Douglas Hultstrand]

Hello,

I am using the lmom and lmomRFA to compute the return frequencies using 
the GEV distribution.Iam trying to generate upper and lower bound 
frequency estimates.

I provided a working example of the code that I am using to estimate the 
upper and lower bounds. Specific questions I have are:

1) Is the methodology appropriate and applied correctly?

2) In this example, are the simulated qhat values better than the actual 
fitted data estimates (GEV)?

_*Code Example Below:*_

library(lmom); library(lmomRFA)
set.seed(1234)

# Example data
max_data <- 
c(11.14,10.95,10.21,9.88,9.85,9.74,9.74,9.73,9.62,8.95,8.38,8.20)
moments = samlmu(max_data, sort.data = TRUE)
parGEV <- pelgev(moments)  # GEV

x <- c(10,25,50,100,500,1000)
Fx <- (1-(1/x))
GEV = Fx
PDS <- 1/(log(x)-log(x-1))

for (i in seq_along(Fx)) {
     GEV[i] = round(quagev(Fx[i], parGEV), 3)
}

################
#### BOUNDS ###
################
# A data sample
zz_gev <- quagev(runif(500), parGEV)

# Compute L-moments of the sample, considered as a 1-site region
rdat_gev <- regsamlmu(zz_gev)

# Fit GEV distribution to the regional L-moments
rfit_gev <- regfit(rdat_gev,"gev")

# Generate simulations of an artificial 1-site region with frequency 
distribution fitted to the actual data
sim_gev <- regsimq(rfit_gev$qfunc, nrec = rdat_gev$n, f = 1 - 1 / x )

# Compute error bounds for quantiles of the site's frequency distribution
CI_gev <- sitequantbounds(sim_gev, rfit_gev)

# 90% Error Bounds/CI
Clwr <- round(CI_gev$bound.0.05, 3)
Cupr <- round(CI_gev$bound.0.95, 3)
qhat <- round(CI_gev$Qhat, 3)

# print data
data.frame(Fx, GEV, Clwr, Cupr, qhat)

####################
#### END BOUNDS ##
####################


#Plot and visualize the data
plot(x, GEV, log="x", ylim=c(10.5,12.5), col="blue")
lines(PDS,GEV, col="blue")
lines(PDS,Clwr, lty=3)
lines(PDS,Cupr, lty=3)
lines(PDS,qhat, col="red", lty=5)

Thanks for your help,

Doug

-- 
-----------------------------------------
Douglas M. Hultstrand, MS
Senior Hydrometeorologist
Applied Weather Associates
Monument, Colorado
voice: 970-682-2462
mobile: 720-771-5840
www.appliedweatherassociates.com
dhultstrand at appliedweatherassociates.com
-----------------------------------------


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