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Table 2 The H −1 ( x ; ξ ) function

From: The Marshall-Olkin extended Weibull family of distributions

Distribution H−1( x; ξ)
Exponential power log x + 1 1 / β λ
Chen [log(x+1)]1/β
Weibull extension λ log x λ + 1 1 / β
Log-Weibull σ log(x)+μ
Kies x 1 / β σ + μ x 1 / β + 1
Gen. Power Weibull β ( x + 1 ) 1 / θ 1 1 / α 1
Gompertz log β x + 1 β
Pham log x + 1 log ( a ) 1 / β