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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