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st: RE: Drawing residuals from a Gumbel distribution


From   "Nick Cox" <n.j.cox@durham.ac.uk>
To   <statalist@hsphsun2.harvard.edu>
Subject   st: RE: Drawing residuals from a Gumbel distribution
Date   Wed, 18 Aug 2010 12:18:43 +0100

To me residuals are what you calculate given data and a model. Reading just the specific paragraphs from the references you helpfully supplied does not make what you want to do entirely clear, but it sounds more as if you want to simulate using error terms drawn from a Gumbel. You can get what might be called unit Gumbel random deviates by e.g. 

gen gumbel = -ln(-ln(runiform())) 

and you can scale those and/or shift them relative to zero if you wish. This recipe follows directly from the form of the quantile function, which is just the inverse of the distribution function given explicitly by your second reference.

Some of the programs in -gumbelfit- from SSC and the short paper 

SJ-7-2  gr0027  . .  Stata tip 47: Quantile-quantile plots without programming
        . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  N. J. Cox
        Q2/07   SJ 7(2):275--279                                 (no commands)
        tip on producing various quantile-quantile (Q-Q) plots

touch on related (but not identical) issues. 

Nick 
n.j.cox@durham.ac.uk 

Mirriam Gee

I am working with a Discrete Labour Supply Model (Binomial logit
model). My question is how can I draw a set of residuals from ‘Extreme
value- type 1 (Gumbel) distribution `  as explained in:

http://ged.u-bordeaux4.fr/ceddt114.pdf
Page 7 (last paragraph)

https://www.gtap.agecon.purdue.edu/resources/download/3712.pdf
Page 11 (last paragraph)


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