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RE: st: A rose by any other name?


From   "Nick Cox" <n.j.cox@durham.ac.uk>
To   <statalist@hsphsun2.harvard.edu>
Subject   RE: st: A rose by any other name?
Date   Wed, 12 Nov 2008 17:48:39 -0000

Thanks to Al and Jeph for the gamma reminders. I was thinking more of a
curve to relate variables, as I should have explained more clearly. 

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

Jeph Herrin

Looks like a gamma distribution g(x,alpha,beta) with alpha=2?
Ie, in Stata

  . gen y = (a/sqrt(b))*gammaden(2,sqrt(b),0,x)

Which doesn't quite answer your question but might lead to
further insights by others.

Nick Cox wrote:
> In a project just starting I shall be playing with various models
> including 
> 
> y = a x exp(-bx) 
> 
> for responses y that are always positive, tend to 0 as x tends to 0
and
> as x becomes arbitrarily large, and in between show a hump, i.e. y
> increases to a maximum and then decreases. 
> 
> Quadratics with a maximum do not have the desired limiting behaviour
and
> go negative somewhere -- even it is outside the observed range. 
> 
> This model comes from ecology (specifically fisheries science) where
it
> is known as the Ricker curve or Ricker model. 
> 
> Ricker, W.E. 1954. Stock and recruitment. Journal of the Fisheries
> Research Board 11: 559-623. 
> 
> This seems too natural a model for its purpose not to crop up
elsewhere
> too. I am curious whether people in different sciences recognise it as
> something also standard in their field under some other name. 
> 
> Googling with the equation was not helpful. 
> 
> (There are naturally other candidate models, but this one looks
> especially nice.) 

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