ThmDex – An index of mathematical definitions, results, and conjectures.
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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}
Also known as
Variance-to-mean ratio, Variance-to-expectation ratio, Dispersion-to-location ratio
Children
▶ D5276: Equidispersed random basic real number
▶ D5277: Index of variation
▶ D5274: Overdispersed random real number
▶ D5275: Underdispered random real number