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RE: st: A rose by any other name?


From   "Feiveson, Alan H. (JSC-SK311)" <Alan.H.Feiveson@nasa.gov>
To   <statalist@hsphsun2.harvard.edu>
Subject   RE: st: A rose by any other name?
Date   Wed, 12 Nov 2008 12:41:40 -0600

To be more precise, the proposed model is a gamma density kernel, not a
bonafide gamma density ,which integrates on 1.  Of course in this
context, the function is used to model nonlinear trend, not a
probability distribution of some random variable.

AL F.

-----Original Message-----
From: owner-statalist@hsphsun2.harvard.edu
[mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of Jeph Herrin
Sent: Wednesday, November 12, 2008 12:13 PM
To: statalist@hsphsun2.harvard.edu
Subject: Re: st: A rose by any other name?

No, your question was clear, and I didn't think I'd answered it - it
would be interesting to know if it crops up elsewhere in nature. I just
thought giving it a name might help jog things along.

cheers,
Jeph

Nick Cox wrote:
> 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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