# What probability distribution is this?

This image show a histogram (200 bins) of accumulated distances from a radar distance meter (very noisy). The peak around 7 meters is an object. At thought this looked kind of like a normal distribution, at least if you ignore values <4m (which for this application is reasonable).

What I am trying to do is to filter out true distances based on the probability distribution.

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Good grief... that indeed is noisy. In any event, if you don't get that many answers here, you could also try @ CrossValidated. –  Ｊ. Ｍ. Dec 13 '10 at 11:44
@J.M. Yeah, very noisy indeed, I can give CV a try too.. –  Theodor Dec 13 '10 at 12:39
I find the title misleading. Maybe you mean "Which probability distribution might this be?". –  Rasmus Dec 13 '10 at 15:02
Thanks for cross-posting on Cross Validated: here's the link to additional answers: stats.stackexchange.com/questions/5430/… –  Jeromy Anglim May 18 '11 at 7:22

If it wasn't for the spike at 0 and the mode at around seven, it would look roughly lognormal to me

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The density function of distance-from-mean of a bivariate normal distribution takes the form $Ax e^{-Bx^2}$, which look pretty much like your noisy graph.

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bivariate? Its really only one dimention - distance. I found that a log - normal distribution (en.wikipedia.org/wiki/Log-normal_distribution) makes a decent fit.. –  Theodor Dec 13 '10 at 12:37
Well, some radar dishes go round and round... –  TonyK Dec 13 '10 at 12:43
Ok, I see your point. Maybe I should have pointed out that it is a 1D radar. –  Theodor Dec 13 '10 at 15:37

I would fit a straight line to the bins near but outside the peak and subtract this from the data, claiming that this level is the background. Then you can do a 2D fit of the Gaussian parameters (mean and sigma) and see how it turns out.

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This is a (tri-modal) mixture distribution.

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