# Relation between the parameter *σ* from log-normal fits and the parameter *κ*_{N} from generalized Pareto fits from numerical simulations.

**A**. *N* = 10^{4} values were drawn from a log-normal distribution with parameters *μ* = 0 and varying *σ* (x-axis). The largest 25, 50, 75, 100% of these values (i.e., 75, 50, 25, 0% truncation) were fitted to a Pareto model with parameters *κ* and *τ*. The plot shows the estimation as a function of *σ*. Averages and standard deviations are taken over 25 independent realizations of the numerical experiment. It shows that limited sampling may cause a to be inferred from values drawn from a log-normal distribution when *σ* is small, here *σ* < 0.5. **B**. Inverse simulation: A truncated log-normal model is fitted to the largest 25, 50, 75, 100% among 500 values (i.e., 75, 50, 25, 0% truncation) drawn from a Pareto model with parameters *τ* = 0.115, *s** = 0.001 and varying *κ* (x-axis). The black dotted line in Fig 4 corresponds to the 25% truncation.

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