Log-Logistic Distribution

Definition

$X\sim Log-logistic(\alpha ,\beta )$ where $\alpha \in {\mathbb{R}}^{+}$ is the shape parameter and $\beta \in {\mathbb{R}}^{+}$ is the Scale Parameter.

Properties

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$f(x)=\frac{(\beta /\alpha )(x/\alpha {)}^{\beta -1}}{(1+(x/\alpha {)}^{\beta {)}^2}},x\in {\mathbb{R}}_0^{+}$