[R] lmomco in gev estimation

[Peter Ehlers]

On 2012-06-19 23:33, Al Ehan wrote:
> Hi guys,
>
> I'm trying to use lmomco package. first I did the manual calculation on
> what is the estimates scale and location parameter given L-CV=0.2, L1=1000
> L-moments and k (shape parameter) =- 0.1. so what i get is:
>
> location: 821.0445
> scale:    260.7590
> shape:    -0.1000
>
> #I assign this as GEV vectors using vec2par
> GEVpara2<-vec2par(c( 821.0445 , 260.7590 ,-0.1),'gev')
>
> #then I generate some data series using the GEV vectors:
> why<-rgev(150,xi=  -0.1000 ,mu= 821.0445,sigma=  260.7590 ) #where xi=shape
> parameter
>
> #then I try to estimate the GEV parameters by L-moments of the generated
> series
> whyr<-pargev(lmom.ub(why))
> whyr
>
> #what I get was a very bias estimate of k (here xi is location)
>           xi       alpha       kappa
> 835.7773068 275.4656939   0.1683969
>
> #even when I replicates it 1000 times and fit into the distribution, the
> shape parameter is still not near to -0.1, but it is going near to the
> nonnegative value (0.1 rather than -0.1)
>
>            xi        alpha        kappa
> 820.89316109 259.45826487   0.09621897
>
> can somebody help me?

It's just a matter of how the shape parameter is defined. Look at
the cdf definition in the lmomco help and compare with that
found in Wiki which presumably is what's being used by whatever
(unstated) package your rgev() is from.
lmomco's shape = -(shape used by rgev).

Peter Ehlers