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
Index of dispersion
Definition D5274
Overdispersed random basic real number
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}
Then $X$ is overdispersed if and only if \begin{equation} \frac{\text{Var} X}{\mathbb{E} X} > 1 \end{equation}