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Different principles are applied to measure the distance or similarity between two distributions using the entropy.
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Distances between two distributions, GMMs, are calculated using the empirical symmetric Kullback-Leibler divergence [28].
In order to evaluate a time-independent metric of the difference between two distributions any norm can be used on Δ t).
Furthermore, the Bhattacharyya coefficient is an approximate measure of the amount of overlapping between two distributions and as such can be used to determine their relative closeness.
The chi square test is used to determine relationship between two distributions.
Chi-square test is a statistical hypothesis test used to determine whether there is a significant difference between two distributions.
We can use the Kullback-Leibler (KL) divergence, a common measure of difference between two distributions.
This test gives a measure of the relative dispersion between two distributions (Goodman 1954).
To more formally assess the convergence of the approximate solution to that of our exact solution, we considered the probabilities of avalanches from size N / 10 to 20N and measured the difference between the distributions using two different metrics.
We chose the value 5 as a threshold as it consistently falls between the two distributions when using the 90th, 95th, and the 99th quantiles; values above 5 were considered truly expressed whereas those below 5 expressed at a low level or not at all.
The difference between the two distributions was assessed using a t-test.
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