Confidence Limits for GPD

[mkskarch]

What steps will reproduce the problem?
1. Fit GPD with 
phat = fitgenpar(data,options)
2. Calculation of CI by [x,xlo,xup] = invgenpar(F,phat,options)


What is the expected output? What do you see instead?
I want to calculate return levels and the corresponding CI bounds.
First, I do a GPD fit with phat = fitgenpar(data,options).
that gives me:
 1. the array with gpd-distribution phat.params
 2. the upper and lower CI phat.upperbound and phat.lowerbound

Now, I calculate the return level for Tr (first approach):
xr = invgenpar(1/(lambda*Tr), phat.params(1), phat.params(2), phat.params(3), 'lowertail',false);
The CI bounds are:
xru = invgenpar(1/(lambda*Tr), phat.upperbound(1), phat.upperbound(2), phat.upperbound(3), 'lowertail',false);
xru = invgenpar(1/(lambda*Tr), phat.lowerbound(1), phat.lowerbound(2), phat.lowerbound(3), 'lowertail',false);

The same could be done (if I understand right) with (second approach):
[xr,xrl,xru] = invgenpar(1/(lambda*Tr, phat, 'lowertail',false)

Now, as expected, the values for xr are the same in the first and in the second approach. But, the values xru and xrl (CI bounds) differ. The second appoach produces very wide bands. 
How comes? To me, it seems that the first approach is correct.


What version of the product are you using? On what operating system?
Newest WAFO 2.5 on MATLAB R2012a on Win7.

[ke]

While not an answer to your question, I will point out that using the 'proflog' option to obtain the confidence intervals produced much narrower intervals for my data and is supposed to be more accurate, according to p. 41 of 'An Introduction to Statistical Modeling of Extreme Values'. I highly recommend this book for understanding the calculations of return period values.

[Value, LowerCi95Percent, UpperCi95Percent] = ...
    invgenpar(ProbabilityReturnPeriod, phat, 'lowertail', false, ...
    'alpha', 0.05, 'proflog', 'true');
% xx-time return level + 95%CI

[Michael Karch]

That's true, thanks for the info. But, how such a huge difference is possible?

2013/4/24 ke <kateed...@hotmail.com>

--
Du mottar denne meldingen fordi du abonnerer på Google-gruppen «wafo».
For å melde seg av denne gruppen og slutte å motta e-poster fra den, send en e-post til wafo+uns...@googlegroups.com.
Hvis du vil legge inn en melding i denne gruppen, kan du sende e-post til wa...@googlegroups.com.
Besøk denne gruppen på http://groups.google.com/group/wafo?hl=no.
Du finner flere alternativer på https://groups.google.com/groups/opt_out.
 
 

[ke]

Here are some reasons given in 'An Introduction to Statistical Modeling of Extreme Values' for why the profile method gives much narrower confidence intervals than the default method used in invgenpar, which is the delta method:
1) The delta method assumes a normal approximation, which may not be correct
2) The profile method allows for greater uncertainty around the higher (more extreme) upper bound than the lower (more reliable) lower bound of the confidence interval
3) The delta method produces a symmetric confidence interval, while the profile method allows for asymmetric confidence intervals, which are often the case
In several points in the book, Coales states that the profile method is more accurate and preferable.
Here is a paper that looked at both methods, http://www2.toulouse.inra.fr/lerna/cahiers2005/05.06.170.pdf