Determine traffic speed distribution while driving I assume that the vehicle speed of cars on a highway is normally distributed around the posted speed limit. I could verify this by sitting by the road with a radar gun and measure vehicle speed for a large number of vehicles passing by.
How could I do this while driving at exactly the speed limit?
Assuming that I have a radar gun in my car, I would measure a positive speed for cars passing me and a negative speed for cars I pass. If I then add my own speed to the observed speed and I should get the same distribution as if I were sitting by the side of the road.
But I feel that I'm missing something: if I keep to the speed limit, then during any period of time, I observe a lot of cars that are either a lot slower than me or a lot faster than me. I'll see a few cars that are a bit slower or a bit faster. However, I'll see (almost) no cars that drive the speed limit (other than the ones in my direct vicinity), because I will never be able to observe them. As a result, I will get a lot of observations in the tail ends of the distribution and almost none near the mean (almost as if sampling from the inverse distribution...?).

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*Can I do a test on my observations to assert whether they fit a Gaussian distribution in the first place?

*If yes, what operation or transformation do I need to apply to my observations to get a Gaussian distribution, if possible?

*What if I can't actually measure speed, but only classify vehicles in bins ("a bit faster/slower, a lot faster/slower, ridiculously fast/slow")?


This crossed my mind the other day while driving and I had the feeling a lot more cars were passing me than I was passing (which is probably just a bias, but nevertheless it triggered this question). I have no background in statistics other than the basics from first year university, so this may be a solved problem and I just don't know what terminology to use to find the solution.

This was a bit of a rabbit hole. None of the existing answers really answered my question, but the comments by "whuber" (pointing to this very similar post) and "Dave" pointed me in the right direction. I'll summarize here what I learned. I simulated everything to check my assumptions.

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*Assuming that vehicle speeds are normally distributed and that distribution is constant in time and space, passing a car or me being passed can be considered a sampling from that distribution.

*The fact that I'm driving does not matter, because, as "Dave" points out, the properties of the normal distribution are invariant for the change of reference (linear operation).

*If I do have a (reliable) radar gun, I can use the Maximum Likelihood Estimator to estimate the parameters of the distribution ($\mu, \sigma$). The fact that I will observe only more much faster/slower vehicles does not really matter, as long as the observations don't skew towards one of those categories (e.g. I get passed a lot by much faster cars, but I don't pass a lot of much slower cars).

*If I don't have a radar gun, I can count the number of cars I pass and that pass me and use that as a z-score (see aforementioned post. In this way, assuming that the distribution is centered around the speed limit and if my speed is not equal to the average speed, I can estimate $\sigma$ from my observations. I tried to combine the results from counting at two different speeds (what "David Smith" suggests) and then estimate both $\mu$ and $\sigma$, but this doesn't give good results, (probably for reasons that are obvious to people more versed in statistics).

