Table 1 Some quantile functions of Y and the domains of T
From: New class of Lindley distributions: properties and applications
Random variable Y | The quantile function QY(p) | Domain of T | |
|---|---|---|---|
(i) | Uniform | p | (0,1) |
(ii) | Exponential | −b log(1−p),b>0 | (0,∞) |
(iii) | Weibull | β(−log(1−p))1/α, β,α>0 | (0,∞) |
(iv) | Log-logistic | a(p/(1−p))1/b, a,b>0 | (0,∞) |
(v) | Logistic | a+b log[p/(1−p)], a,b>0 | (−∞,∞) |
(vi) | Cauchy | tan(π(p−0.5)) | (−∞,∞) |