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Calculating the Error

There remains an uncertainty which is due to the varying value of the graph length. That error propagates to the overall, larger-scale calculation as listed in Equation 1. This leads to imbalance in the value of entropy. The error can be estimated in the following way: for each of the entropy 'sub-components' above, entropy is estimated which is dependent on the graph distance. Thus, considering the standard error

$$\sigma=\frac{L_{\gamma}}{\sqrt{N-1}}$$ (3)

where N is the number of instantiation used for error estimation. In line with rules for error propagation in logarithms

$$\sigma_{propagated}=\frac{log(\sigma)}{L_{\gamma}}$$ (4)

This gets applied to both cloud comparisons. Then, in order to combine the contribution of both entropies

$$\sigma_{total}=\sqrt{\sigma_{S_{0}\Rightarrow T}^{2}+\sigma_... ...}-2\sigma_{S_{0}\Rightarrow S_{i}}\sigma_{S_{0}\Rightarrow T}}$$ (5)

$H(Z_{n})$ together with $\sigma_{total}$ provide the final estimation of entropy and its level of (un)certainty.