Which distribution has the following variance formula?

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Given a set of data $x_i$, for $i=1\ldots N$. I know their variance is calculated by

$$\sigma^2 = A \sum_{i=2}^N \ln^2\left(\frac{x_i}{x_{i-1}}\right)$$

where $A$ is a constant.

how can I determine how my data set is distributed?