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.
In this case, noting that F−1(y) = exp ( m + √ 2s erf−1(2y− 1) ) (Table I), and that Φ(xG) is given in Eq
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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.