[R] Difference in Generalized Extreme Value distribution parameter estimations using lmom and fExtremes

[Amelia Marsh]

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