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\[  \Delta_{JS}(A;B) = \sqrt{JS(A;B)}  \]  is a metric, i.e. metric; that is,  it is positive $\big[\Delta_{JS} \ge 0\big]$, symmetrical $\big[\Delta_{JS}(A;B) = \Delta_{JS}(B;A)\big]$ and satisfies the triangular inequality $\big[\Delta_{JS}(A;B) \le \Delta_{JS}(A;C) + \Delta_{JS}(B;C)\big]$. We will use this metric of the distance between probability density functions in the following analysis. Finally, we note that the definition of entropy involves knowledge of the probability density function and there are well-known problems in the estimation of the underlying pdf from a single sample of variables from the distribution. This will be discussed below.