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st: RE: A rose by any other name?


From   "Feiveson, Alan H. (JSC-SK311)" <Alan.H.Feiveson@nasa.gov>
To   <statalist@hsphsun2.harvard.edu>
Subject   st: RE: A rose by any other name?
Date   Wed, 12 Nov 2008 11:33:34 -0600

This is special case of a gamma density function. 

f(x) = C(x^k)*exp(-a*x)

Al F.

-----Original Message-----
From: owner-statalist@hsphsun2.harvard.edu
[mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of Nick Cox
Sent: Wednesday, November 12, 2008 9:49 AM
To: statalist@hsphsun2.harvard.edu
Subject: st: A rose by any other name?

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.) 

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

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