Index: The Book of Statistical ProofsGeneral Theorems ▷ Probability theory ▷ Measures of statistical dispersion ▷ Full width at half maximum

Definition: Let $X$ be a continuous random variable with a unimodal probability density function $f_X(x)$ and mode $x_M$. Then, the full width at half maximum of $X$ is defined as

\[\label{eq:FWHM} \mathrm{FHWM}(X) = \Delta x = x_2 - x_1\]

where $x_1$ and $x_2$ are specified, such that

\[\label{eq:x12} f_X(x_1) = f_X(x_2) = \frac{1}{2} f_X(x_M) \quad \text{and} \quad x_1 < x_M < x_2 \; .\]

Metadata: ID: D91 | shortcut: fwhm | author: JoramSoch | date: 2020-08-19, 05:40.