ThmDex – An index of mathematical definitions, results, and conjectures.
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Probability density function
Definition D2864
Real gaussian density function
Formulation 0
The real gaussian density function with parameter $(\mu, \sigma) \in \mathbb{R} \times (0, \infty)$ is the D4364: Real function \begin{equation} \mathbb{R} \to \mathbb{R}, \quad x \mapsto \frac{1}{\sqrt{2 \pi \sigma^2}} \exp \Bigg[ - \frac{1}{2} \Bigg( \frac{x - \mu}{\sigma} \Bigg)^2 \Bigg] \end{equation}
Formulation 1
The real gaussian density function with parameters $\mu \in \mathbb{R}$ and $\sigma \in (0, \infty)$ is the D4364: Real function \begin{equation} \mathbb{R} \to \mathbb{R}, \quad x \mapsto \frac{1}{\sqrt{2 \pi \sigma^2}} e^{- \frac{1}{2} \big( \frac{x - \mu}{\sigma} \big)^2} \end{equation}
Children
D2718: Euclidean real gaussian density function
D2719: Standard real gaussian density function