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Relation between the parameter σ from log-normal fits and the parameter κN from generalized Pareto fits from numerical simulations.

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posted on 2021-03-25, 20:08 authored by Steven Schulz, Sébastien Boyer, Matteo Smerlak, Simona Cocco, Rémi Monasson, Clément Nizak, Olivier Rivoire

A. N = 104 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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