778 B
778 B
Landau PDF
A pathological distribution
Because of its fat tail:
\begin{align*} E[x] &\longrightarrow + \infty \ V[x] &\longrightarrow + \infty \end{align*}
. . .
No closed form for parameters.
Landau median
The median of a PDF is defined as:
Q_L(m) = \frac{1}{2}
. . .
- CDF computed by numerical integration,
- QDF computed by numerical root-finding (Brent)
m_L = 1.3557804...
Landau mode
- Maxmimum
\quad \Longrightarrow \quad \partial_x M(\mu) = 0, - Computed by numerical minimization (Brent)
\mu_L = − 0.22278...
Landau FWHM
\text{FWHM} = x_+ - x_- \with L(x_{\pm})
= \frac{L_{\text{max}}}{2} = \frac{L(\mu_L)}{2}
- Computed numerically (Brent)
\text{FWHM}_L = 4.018645...