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Table 1 Quantile functions for different Y distributions

From: The generalized Cauchy family of distributions with applications

Y Q Y (p)
(a) Uniform p
(b) Exponential −log(1−p)
(c) Log-logistic p / (1−p)
(d) Logistic log[p /(1−p)]
(e) Extreme value log[−log(1−p)]
(f) Fréchet −1/log(1−p)