Table 1 Inverse function x=H −1(y) for some EG models
Distribution | x=H −1(y) |
|---|---|
Exponential power | \(\frac {[\log (y+1)]^{1/\beta }}{\lambda }\) |
Chen | \(\left [\log (y+1)\right ]^{1/\beta }\) |
XTG | \(\lambda \big [\log \big (y/\lambda +1\big)\big ]^{\frac {1}{\beta }}\) |
Log-Weibull | \(\sigma \log (y)+\mu \) |
Kies | \(\frac {y^{1/\beta }\sigma +\mu }{y^{1/\beta }+1}\) |
Generalized power Weibull | \(\beta \left [(y+1)^{1/\theta }-1\right ]^{1/\alpha _{1}}\) |
BLZ | \(\frac {\log (t)\pm \sqrt {\left [\log (y)\right ]^{2}+4\alpha _{1}\beta }}{2\alpha _{1}}\) |
Gompertz | \(\frac {\log \left (\alpha _{1}y+1\right)}{\alpha _{1}}\) |
Pham | \(\Big [\frac {\log (1+y)}{\log (a_{1})}\Big ]^{1/\alpha _{1}}\) |