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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)