Find the period in a random distribution

I have objects which are randomly distributed in the X axis. The objects have a periodic (m) distribution with a slight variation of their position around multiples of m.

The graph here shows a distribution for m=100.

Is there a way to calculate m using the statistics of distribution?

Thanks!

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Do you know the error distribution? If so, for example, it's a 0 mean Gaussian with variance sigma^2, then you can calculate the likelihood of the data as a function of the unknown period m. Once you can do this you can try to solve an optimization and find the period that has maximum likelihood.

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