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 - 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. Also, 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?
not an expert, but maybe the ex-gaussian (gaussian plus exponential distribution)?
From the last link:
In the framework of cognitive processes, this convolution can be seen as representing the overall distribution of RT [Response Time] resulting from two additive or sequential processes. As proposed by Luce (1986, chap. 6), the exponential process can be seen as the decision component, i.e., the time required to decide which response to make, while the Gaussian component can be conceptualized as the transduction component, i.e., the sum of the time required by the sensory process and the time required to physically make the response.
The Weibull distribution  is a generalization of the exponential distribution that is often used in time-to-event analysis. Also note that you can use non-parametric methods like Kaplan-Meier estimates that fit the distribution you actually have, instead of trying to fit into an arbitrary category.