Distribution

Mixing proportion

Mixing components

Failure rate

Parameters

shape

location

GLD ( $\theta \mathrm{,}\gamma \mathrm{,}\alpha$ )

$\frac{\theta }{\theta +\gamma }$

gamma ( $\alpha \mathrm{,}\theta$ ), gamma ( $\alpha +\mathrm{1,}\theta$ )

increasing

$\theta \mathrm{,}\gamma \mathrm{,}\alpha$

-

bathtub

decreasing

TwPLD ( $\theta \mathrm{,}\alpha$ )

$\frac{\theta }{\theta +\alpha }$

exponential ( $\theta$ ), gamma ( $\mathrm{2,}\theta$ )

increasing

$\theta \mathrm{,}\alpha$

-

NGLD ( $\theta \mathrm{,}\alpha$ )

$\frac{\theta }{\theta +1}$

gamma ( $\alpha \mathrm{,}\theta$ ), gamma ( $\alpha -\mathrm{1,}\theta$ )

increasing

$\theta \mathrm{,}\alpha$

-

LwLD ( $\theta \mathrm{,}\alpha \mathrm{,}\beta$ )

$\frac{\theta }{\theta +\alpha }$

exponential ( $\theta \mathrm{,}\beta$ ), gamma ( $\mathrm{2,}\theta \mathrm{,}\beta$ )

increasing

$\theta \mathrm{,}\alpha$

$\beta$

NGTwPLD ( $\theta \mathrm{,}\alpha$ )

$\frac{\theta }{\theta +1}$

exponential ( $\theta$ ), gamma ( $\alpha \mathrm{,}\theta$ )

increasing

$\theta \mathrm{,}\alpha$

-

bathtub

decreasing

LGAD

$\frac{{\theta }^2}{{\theta }^2+\eta }$

exponential ( $\theta \mathrm{,}\beta$ ) and gamma ( $\mathrm{3,}\theta \mathrm{,}\beta$ )

increasing

$\theta \mathrm{,}\eta$

$\beta$

bathtub

TwPD ( $\theta \mathrm{,}\alpha$ )

$\frac{\theta -2\alpha }{\theta -\alpha }$

gamma ( $\alpha \mathrm{,}\theta$ ), gamma ( $\alpha +\mathrm{1,}\theta$ )

increasing

$\theta \mathrm{,}\alpha$

-

bathtub