R help - Jan 2017 - Difference in Generalized Extreme Value distribution parameter estimations using lmom and fExtremes

Dear R forum

I have following dataset

amounts =
c(2803102.248,1088675.278,10394575.14,1007368.396,1004871.328,1092956.088,1020110.818,997371.4487,1000904.154,998105.9744,997434.3006,1080067.258,997594.7992,1000871.015,1001321.094,1000713.448,997591.2307,1469501.54,1066924.393,1074918.566,998628.6216,1002538.482,1056969.243,997386.2638,1.36951E+11,997996.9907,1001257.498,998297.1517,5253186.541,1005503.303,997785.7993,997327.4303,1037039.271,997353.5027,998297.0299,1072558.563,2713147.593,997679.0361,1015856.216,1424576097,999165.4936,998038.8554,3221340.057,1009576.799,5.84277E+12,18595873.96,1054794.099,1005800.558,997533.8031,997347.4897,2208865120,4224689.441,997660.4156,997325.1814,46809107.76,1200682.819,998921.9662,997540.1311,997594.3338,1109023.716,1007961.274,1939821.599,998260.2296,175808356.8,1005375.437,997412.0361,997383.9452,998863.5354,1554312.55,997791.3639,997355.1921,997476.2689,14557283.34,997937.3784,1013997.695,1006244.593,999265.8925,1052001.211,1005484.306,1258924.294,998740.9426,997896.5631,3613729.605,1000823.697,1656621.398,997874.4055,1056353.896,1000380.152,997576.3836,997442.5109,998563.4918,1032782.759,1010023.106,998578.6725,997344.4766,997310.5771,1002905.434,86902124.97,998396.3911,1245564.907)


Using this dataset, I am trying to estimate the parameter values of Extreme
Value Distribution. I am using the libraries lmom and fExtremes as follows:


library(lmom) 
library(fExtremes)

#____________________________________________________________ 


# Parameter estimation : Using lmom 


lmom <- samlmu(amounts) 
(parameters_of_GEV_lmom <- pelgev(lmom)) 


# OUTPUT: 
> parameters_of_GEV_lmom <- pelgev(lmom); parameters_of_GEV_lmom 

xi                      # Location Parameter
8.883402e+06

alpha                 # Scale Paramter
5.692228e+07 

k                       # Shape Parameter
-9.990491e-01 



# ________________________________________________________________________



# Parameter estimation : Using fExtremes

(parameters_of_GEV_fExtremes <- gevFit(amounts, type = "pwm")) 

# OUTPUT: 

Title: 
GEV Parameter Estimation 

Call: 
gevFit(x = amounts, type = "pwm") 

Estimation Type: 
gev pwm 

Estimated Parameters: 


xi                        # Shape Parameter
9.990479e-01


mu                       # Location Parameter
8.855115e+06


beta                      # Scale paramter
5.699583e+07 



# __________________________________________________________________

While it is obvious that the parameter values will differ as lmom is using L
moments and fExtremes is using Probability Weighted Moment, my concern is about
the shape parameter. The value of shape parameter is same across all methods
except the sign.

While lmom estimates shape parameter = -0.99905, fExtremes estimates shape
parameter = 0.99905. When I have used Statistical software to estimate the
parameters, I got the parameter values exactly tallying with what lmom is
generating but scale parameter was equal to 0.99905 (Positive value same as
fExtremes value) and not -0.99905 which is generated by lmom libraray.

Can some one guide me.


With regards

Amelia