How can i find out closest lognormal distribution parameters from a GEV distributed data in R

The question is a bit weird so i'll open it up. So i have a table of return periods for different amounts of rain. The table has been made using GEV distribution on known data and then the mean and confidence intervals are calculated for different return periods.

I need to recreate this curve closely as possible in another program that does not have GEV-distribution so i will have to use lognormal in this case. How can i get the parameters for a lognormal distribution that would be close to the GEV curve. I also don't have the original datapoints, just the data from the curve.

With the R code below, I found the lognormal distribution which minimizes $$\sum(\log_{10}(\text{actual period})-\log_{10}(\text{predicted period}))^2.$$ This gives $$\mu=2.994$$, $$\sigma=.0516$$, and the following curiously well-fitting graph:

periods <- c(10, 25, 50, 100, 200, 300, 500, 10^3, 10^4,
10^5, 10^6, 10^7, 10^8, 10^9)
precips <- c(44, 53, 60, 68, 76, 81, 87, 96, 131, 174, 225,
288, 365, 458)

periodfits <- function(params){1/(1-plnorm(precips,
params[[1]], params[[2]]))}
score      <- function(params){sum((log10(periods) -
log10(periodfits(params)))^2)}

par <- optim(c(1,1), score)$par print(par) plot( precips, log10(periods)) points(precips, log10(periodfits(par)), col=2)  • What if i need to change the periods to probability. So changing to 10^-1, 10^-2., 10^-3..etc. Can't seem to get it to work as it does not want to go under 0 if using the lognormal scale. Aug 16, 2021 at 13:51 • If the transformations$\mu_{prob}=-\mu_{period}$or$prob=1/period\$ are causing difficulties, I'm not sure what to say. But if there's anything in the answer that you found useful, then an upvote would be nice! Aug 16, 2021 at 17:17