A monotone transformation of a Gaussian process alters its autocorrelation through a distribution-specific function, and the power-law exponent survives when the first-order term of that function dominates.
As can be seen in Table II, the standardized forms of the Weibull and Pareto distributions have shape parameters, δ and ε respectively, which control the tail behavior
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Transforming Gaussian correlations. Applications to generating long-range power-law correlated time series with arbitrary distribution
A monotone transformation of a Gaussian process alters its autocorrelation through a distribution-specific function, and the power-law exponent survives when the first-order term of that function dominates.