Parameter Estimation Gumbel Distribution 12182021 Dept of Bioenvironmental

Parameter Estimation Gumbel Distribution 12/18/2021 Dept. of Bioenvironmental Systems Engineering, National Taiwan University 1

12/18/2021 Dept. of Bioenvironmental Systems Engineering, National Taiwan University 2

12/18/2021 Dept. of Bioenvironmental Systems Engineering, National Taiwan University 3

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• ks. test(x, "pgumbel", loc=loc. x, scale=scale. x, alternative=“two. sided”) • ks. test(x, "pnorm", mean(x), sd(x), alternative="two. sided") 12/18/2021 Dept. of Bioenvironmental Systems Engineering, National Taiwan University 7

R Package - kolmim • Cumulative probability of the test statistic Dn can be obtained using the function pkolm 12/18/2021 Dept. of Bioenvironmental Systems Engineering, National Taiwan University 8

One-Sample KS (GOF) Test in R • • • • x=scan("WP 2_Prob 2. csv", sep=", ") library(kolmim) nd=length(x) # ----------------------------# Defining the distribution for Ho: Gumbel scale. x=sqrt(6)*sd(x)/pi # Parameter estimation MOM loc. x=mean(x)-0. 5772*scale. x # ----------------------------Gumbel. ks=ks. test(x, "pgumbel", loc=loc. x, scale=scale. x, alternative="two. sided") # Gumbel. ks=ks. test(x, "pnorm", mean(x), sd(x), alternative="two. sided") Gumbel. ks v=1: 200/500 plot(v, sapply(v, function (v) pkolm(v, nd)), type='l', col="blue") abline(v=Gumbel. ks[1]) 1 -pkolm(Gumbel. ks[1], nd) # p-value 12/18/2021 Dept. of Bioenvironmental Systems Engineering, National Taiwan University 9

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