Distributions

PDFs

EE

$f\left(x\right)=\delta \lambda {\left(1-{\text{e}}^{-\lambda x}\right)}^{\delta -1}{\text{e}}^{-\lambda x},x>0$

ME

$f\left(x\right)=\frac{\lambda {\alpha }^{\beta }{\text{e}}^{-\lambda x}}{\left(1+{\alpha }^{\beta }\right){\left(1-\frac{{\text{e}}^{-\lambda x}}{1+{\alpha }^{\beta }}\right)}^2},x>0$

KE

$f\left(x\right)=\alpha \beta \lambda {\text{e}}^{-\lambda x}{\left(1-{\text{e}}^{-\lambda x}\right)}^{\alpha -1}{\left(1-{\left[1-{\text{e}}^{-\lambda x}\right]}^{\alpha }\right)}^{\beta -1},x>0$

E

$f\left(x\right)=\lambda {\text{e}}^{-\lambda x},x>0$