I am trying to model the time lapse between when a user sees an ad and when they call the advertiser (presuming they do).

I have two issues:

  1. Part of the data seems exponential, but I am wondering if there is a similar distribution with an extra parameter because I cannot quite get it to fit.
  2. The peak does not occur at t = 0 but rather at t = 30s or so - obviously people do not call immediately, as there is a necessary physical delay between seeing the ad and picking up the phone. But some people do call at 2 seconds, or 3, etc, and as I mentioned, the peak is at 30.

Is there a simple way to model this?

asked Aug 14 '10 at 14:39

george%20s's gravatar image

george s
517810

edited Aug 18 '10 at 17:11

Joseph%20Turian's gravatar image

Joseph Turian ♦♦
579051125146


4 Answers:

Maybe a gamma distribution? It looks like an exponential, but has a non-zero mean.

answered Aug 14 '10 at 14:57

Alexandre%20Passos's gravatar image

Alexandre Passos ♦
2554154278421

How about an exGaussian distribution? It is the difference between a normal distribution and an exponential distribution and people use it to model reaction times in psychophysics.

answered Aug 16 '10 at 13:56

Ama%C3%A7%20Herda%C4%9Fdelen's gravatar image

Amaç Herdağdelen
1763813

edited Aug 16 '10 at 14:00

It is probably overkill for your application, but there is an excellent book on reaction times. It's a rare careful and thorough work through of reaction times, and the kind of things you can do with them (including the statistical approaches). I came across it after proposing to some psycho-linguist friends the idea of using hazard functions to model how long you'll wait to see a response.

answered Aug 16 '10 at 18:31

Vicente%20Malave's gravatar image

Vicente Malave
355137

I heard about doubly-exponential or ex-gaussian distribution for RTs data (especially for spotting outliers), but you might have a look at the following papers (all available on the web):

  • Effective analysis of reaction time data, Whelan R
  • Schmiedek et al. Individual differences in components of reaction time distributions and their relations to working memory and intelligence. Journal of experimental psychology General (2007) vol. 136 (3) pp. 414-29
  • Ratcliff. Methods for dealing with reaction time outliers. Psychological Bulletin (1993) vol. 114 (3) pp. 510-32
  • Ashby. Testing the assumptions of exponential, additive reaction time models. Memory & cognition (1982) vol. 10 (2) pp. 125-34

With regard to your original question, I agree with Alexandre that it is worth to look at a Gamma distribution.

answered Aug 18 '10 at 07:19

chl's gravatar image

chl
9138

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