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.

Consider doing your experiment at least twice at two different speeds, eg, 65 mph and 70 mph. (This is in the US. Elsewhere use two speeds in kph.)
Each experiment gives you information about the number or fraction of cars traveling at the other speed, as well as twice as much information about all the other speeds. Weighting the numbers at these two speeds would be appropriate, either fifty-fifty or taking the two totals into account.
I have counted the numbers of cars traveling faster or slower than I was on the tri-state toll road around Chicago. I concluded that the median speed was 70 miles per hour when the speed limit was 55 mph for nearly the total distance. During rush hours, of course, the median can be as low as 10 mph, or less, for long stretches.
I do not know how accurate radar guns are in moving cars. It would be worth finding out if there is a bias, either due to angle of measurement or due low differences in speed. I do not think you have to take relativity due to moving traffic into account.
Happy measurement.
