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

[Chris R. Sims]

Rhiannon,

When I do the transformation I get the following for the PDF of  
retrieval latencies, conditional on a chunk being selected:

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x is the retrieval time, F is the latency scale factor, A is the  
activation of the chunk, and b is the shape parameter of the logistic  
noise distribution.  The integral of this adds to one, so I'm fairly  
sure this is correct. Is this also what you obtained?

Also, I think there is some ambiguity about the distribution of  
retrieval times.  The above equation gives the distribution for one  
chunk, conditional on it being selected.  So if you repeatedly  
retrieved a chunk with a constant base level activation, you would  
get the above distribution due to noise.

I think (but correct me if I'm wrong) that the Gumbel or extreme  
value distribution is used to approximate the retrieval times  
selecting from a set of identically distributed chunks.  In this  
case, the Weibull is not conditional on a particular chunk being  
selected, but only on there not being a retrieval failure.  So in  
summary, there's a distribution of times for repeatedly retrieving  
the same chunk, described by the equation above, and then there's a  
distribution of times for selecting from a pool of chunks, described  
by the Weibull approximation.  Unfortunately I don't have a copy of  
'Atomic Components' on hand, so this is based on my rapidly decaying  
memory for chapter 3.

Best,
-Chris


On Dec 20, 2005, at 8:35 PM, 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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