ThmDex – An index of mathematical definitions, results, and conjectures.
Formulation F11862 on D5901: Logistic random real number
Formulation 0
Let $\log$ be the D865: Standard natural real logarithm function.
Let $U \in \text{Uniform}(0, 1)$ be a D4624: Standard unsigned uniform random real number.
A D3161: Random real number $X \in \text{Random}(\mathbb{R})$ is a logistic random real number with parameters $\mu \in \mathbb{R}$ and $\nu \in (0, \infty)$ if and only if \begin{equation} X \overset{d}{=} \mu + \nu \log \frac{U}{1 - U} \end{equation}