ThmDex – An index of mathematical definitions, results, and conjectures.
Set of symbols
Deduction system
Zermelo-Fraenkel set theory
Binary cartesian set product
Binary relation
Simple map
Simple function
Measurable simple complex function
Simple integral
Unsigned basic integral
Unsigned basic expectation
Basic expectation
Random real number moment
Random real number central moment
Absolute central moment
Random real number variance
Definition D3844
Index of dispersion
Formulation 0
Let $X \in \text{Random}(\mathbb{R})$ be a D3161: Random real number such that
(i) \begin{equation} \mathbb{E} |X|^2 < \infty \end{equation}
(ii) \begin{equation} \mathbb{E} X \neq 0 \end{equation}
The index of dispersion of $X$ is the D993: Real number \begin{equation} \text{Disp} X : = \frac{\text{Var} X}{\mathbb{E} X} \end{equation}
Equidispersed random basic real number
Index of variation
Overdispersed random basic real number
Underdispered random basic real number