[ACT-R-users] Question about chunk recall times

[John Anderson]

Rhiannon:

I felt motivated to look at this at home without my stat books in 
hand:  As much as this is discussed it is in the Appendix of Chapter 
3.  Looking at this it seems to me that the claim is that the Gumbel 
(or double exponential as I have since learned to call it) is related 
to the Weibull by this transformation.    Now, one potential for 
confusion is the Gumbel is not really the activation distribution but 
an approximation as discussed in that Appendix.  And I think as you 
assert, it is conditional on the chunk being chosen.

However, overlooking this detail, it still seems to me at home that 
Gumbel is related to the Weibull as claimed.   However, I would be 
more than happy if you could show me how to better present this in 
future efforts or indeed show me otherwise.  I am just upstairs.  I 
was hoping your efforts would improve my education.

--John

At 8:35 PM -0500 12/20/05, Rhiannon L Weaver wrote:
>In the Atomic Components of thought book it is mentioned that using the
>equation RT = Fe^{-(A + epsilon)} yields a Weibull distribution for chunk
>recall times (where RT = "retrieval time" and A + epsilon = noisy
>activation of the chunk). 
>
>Can someone point me to a proof of this?  I am wondering if the
>distribution arises conditional on the chunk being chosen?  If I do a
>straight transformation of variables assuming the variation comes from the
>logistic epsilon, I don't get a Weibull distribution, I get something
>else, something that looks like quadratic decay in time.  Help?
>
>Thanks,
>-Rh
>
>Rhiannon Weaver
>PhD student, Statistics
>Carnegie Mellon University
>
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John R. Anderson
Carnegie Mellon University
Pittsburgh, PA 15213

Phone: 412-268-2788
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email: ja at cmu.edu
URL:  http://act.psy.cmu.edu/