Often, the distribution of some variants will vary with respect to time. Whether there exists some traditional method or function to measure how a collection of samples sampled in different times follow an identical distribution.
For example, I have two samples, x1, sampled in TIME1, and x2, sampled in TIME2. And the function is f. If the distribution remains the same in both TIME1 and TIME2, then f(x1, x2) = 0; while if the distribution in TIME1 is quite different from that in TIME1, then f(x1, x2) = 1. So what is the f?
You may want to consider a Kolmogorov–Smirnov test. The test considers whether or not distributions of sample data differ.
By checking how well the moments, computed from the samples, satisfy the identities that express the fact that the moments are those of the same distribution (assuming the moments of the distribution exist). For instance, if ρ(x)=exp(-S(x)), is the distribution, it's easy to deduce that its moments satisfy the identities k=, up to surface terms. The Gaussian distribution is a special case, where S(x)=quadratic polynomial in x. What's necessary is that S(x) be bounded from below and S(x) -> +oo, as x->+/-oo.
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