[R] Fitting GUMBEL Distribution - CDF function ISSUE

[Maithili Shiva]

Dear R helpers

I am trying to fit the Gumbel distribution to a data. I am using lmom package. I am getting problem in Cumulative Distribution Function of Gumbel distribution as I am getting it as a series of 0's and 1's thereby affecting the P P Plot. My R code is as follows.


 library(quantreg)
 library(RODBC)
 library(MASS)
 library(actuar)
 library(lmom)

 x <- c(986.78,1067.76,1046.47,1034.71,1004.53,1007.89,964.94, 1060.24, 1188.07, 1085.63,988.33,972.71, 1177.71,972.48,1203.20, 1047.27,1062.95, 1113.65, 995.97, 1093.98)


#Estimating the parameters for GUMBEL distribution

 N                    <- length(x)

 lmom 		    <- samlmu(x); lmom

 parameters_of_GUMBEL <- pelgum(lmom); parameters_of_GUMBEL
 

 # Parameters are xi =  1019.4003   alpha =   59.5327



 # _____________________ P - P Plot ________________________
 
 e        <- c(1:N)

 f        <- c((e-.5)/N)

 Fx       <- cdfgum(x, para = parameters_of_GUMBEL)
 
 g        <- sort(Fx)
 
 png(filename = "GUMBEL_P-P.png")
 
 a <- par('bg'= "#FFFFCC")
 
 plot (f,g,bg=a,fg= "#804000",main ="P-P Plot", ylab=" Cumulative Distribution Function", xlab="i", font.main=2, cex.main=1,col="#999966",bty = "o",col.main="black",col.axis="black",col.lab ="black")

 abline(rq(g ~ f, tau = .5),col="red")

 dev.off()


# Fx RETURNS    0 1 1 1 0 0 0 1 1 1 0 0 1 0 1 1 1 1 0 1  and Thus plot is not proper

 


Please guide me as where I am going wrong.

With regards


Maithili