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
[email protected]
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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