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.

I think your goal of characterizing the distribution of highway speeds while on the highway yourself is doomed to fail, as you've rightly pointed out that you'll never pass anyone going the same speed as you. Suppose you're in an autonomous car with the front and back windshield blacked out, so that you can only observe cars when you pass them. It's impossible for you to tell if the highway is completely empty, or if it's full of cars moving the exact same speed as you. If you do pass or are passed by some other cars, it'll be impossible to know if those are the only other cars and very common speeds, or if they're a minority of people not driving the same speed as you. You might have some additional mileage if you're able to assume that speeds are in fact normally distributed around your own speed, as you can get a sense of a variance in speed from the cars that do pass you, but I don't think you can get very far without some means of reasoning about the number of people driving the same speed as you, which the distributional assumption allows.
