Definition: Full width at half maximum
Index: The Book of Statistical Proofs ▷ General Theorems ▷ Probability theory ▷ Measures of statistical dispersion ▷ Full width at half maximum
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Metadata: ID: D91 | shortcut: fwhm | author: JoramSoch | date: 2020-08-19, 05:40.
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
\[\label{eq:x12} f_X(x_1) = f_X(x_2) = \frac{1}{2} f_X(x_M) \quad \text{and} \quad x_1 < x_M < x_2 \; .\]- Wikipedia (2020): "Full width at half maximum"; in: Wikipedia, the free encyclopedia, retrieved on 2020-08-19; URL: https://en.wikipedia.org/wiki/Full_width_at_half_maximum.
Metadata: ID: D91 | shortcut: fwhm | author: JoramSoch | date: 2020-08-19, 05:40.