Table 1 Exponential, Weibull and log-logistic distributions

f (x) = λ e ^-λx

$\left(x\right)=\lambda \beta {(\lambda x)}^{\beta -1}{e}^{(-{(\lambda x)}^{\beta })}$

$f\left(x\right)=\frac{\lambda \beta {(\lambda x)}^{\beta -1}}{{(1+{(\lambda x)}^{\beta })}^2}$

x > 0

x > 0

x > 0

λ > 0

λ > 0

λ > 0

β > 0

β > 0