sections: rite sections 2 and 4

slides/sections/2.md

@@ -1,7 +1,7 @@
 # Landau PDF
 
 
-## Pathological probability distribution
+## A pathological distribution
 
 Because of its fat tail:
 
@@ -10,23 +10,48 @@ Because of its fat tail:
   V[x] &\longrightarrow + \infty
 \end{align*}
 
+. . .
+
 No closed form for parameters.
 
+
 ## Landau median
 
 The median of a PDF is defined as:
 
 $$
-  Q_L(x) = \frac{1}{2}
+  Q_L(m) = \frac{1}{2}
 $$
 
+. . .
+
 - CDF computed by numerical integration,
 - QDF computed by numerical root-finding (Brent)
 
-hence:
-
 $$
   m_L = 1.3557804...
 $$
 
-o
+
+## 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)
+
+$$
+  \text{FWHM}_L = 4.018645...
+$$

slides/sections/4.md

@@ -1,8 +1,9 @@
 # Data sample
 
-## Data sample
 
-The $M(x)$ most similar to $L(x)$ is found by imposing:
+## PDF parameters
+
+A $M(x)$ similar to $L(x)$ can be found by imposing:
 
 - equal mode
 $$
@@ -19,3 +20,16 @@ $$
 $$
   \implies \sigma_M \approx 1.1191486
 $$
+
+
+## PDF parameters
+
+:::: {.columns}
+:::  {.column width=50%}
+  ![](images/both-pdf-bef.pdf)
+:::
+
+:::  {.column width=50%}
+  ![](images/both-pdf-aft.pdf)
+:::
+::::