ThmDex – An index of mathematical definitions, results, and conjectures.
▼ Set of symbols
▼ Alphabet
▼ Deduction system
▼ Theory
▼ Zermelo-Fraenkel set theory
▼ Set
▼ Subset
▼ Power set
▼ Hyperpower set sequence
▼ Hyperpower set
▼ Hypersubset
▼ Subset algebra
▼ Subset structure
▼ Measurable space
▼ Measure space
▼ Pushforward measure
▼ Distribution measure
▼ Probability distribution measure
▼ Probability distribution function
Definition D3793
Exponential probability distribution function
Formulation 0
The exponential probability distribution function with parameter $\theta \in (0, \infty)$ is the D4367: Unsigned real function \begin{equation} \mathbb{R} \to [0, 1], \quad x \mapsto (1 - e^{- \theta x}) I_{x \geq 0} \end{equation}
▶▶▶
Comment 0
$I_{x \geq 0}$ denotes an D41: Indicator function where the convention N641: Denoting the basis set for an indicator function as a predicate statement has been applied.
Formulation 1
The exponential probability distribution function with parameter $\theta \in (0, \infty)$ is the D4367: Unsigned real function \begin{equation} \mathbb{R} \to [0, 1], \quad x \mapsto \begin{cases} 1 - e^{- \theta x}, \quad & x \in [0, \infty) \\ 0, \quad & x \in (-\infty, 0) \end{cases} \end{equation}