Table 1:

Common Location-Scale Models used in Life Testing

Distribution	$F_0\left(x\right)$	$f_0\left(x\right)$	$Q_0\left(u\right)$
Normal	$\Phi \left(x\right)$	$\text{exp}\left(-x^2/2\right)/\sqrt{2\pi }$	${\Phi }^{-1}\left(u\right)$
Logisitic	$1/\left(1+\text{exp}\left(-x\right)\right)$	$\text{exp}\left(x\right)/{\left(1+\text{exp}\left(x\right)\right)}^2$	$\text{log}\left(u/\left(1-u\right)\right)$
Extreme Value	$1-\text{exp}\left(-\text{exp}\left(x\right)\right)$	$\text{exp}\left(-\text{exp}\left(x\right)+x\right)$	$\text{log}\left(-\text{log}\left(1-u\right)\right)$