sections: write a lot

slides/sections/4.md

@@ -71,7 +71,7 @@ $$
   f_\varepsilon(x) = \frac{1}{N\varepsilon} \sum_{i = 1}^N
   G \left( \frac{x-x_i}{\varepsilon} \right)
   \with
-  \varepsilon = 0.63 \, S_N
+  \varepsilon = 0.88 \, S_N
   \left( \frac{d + 2}{4}N \right)^{-1/(d + 4)}
 $$
 

slides/sections/6.md

@@ -1,13 +1,19 @@
 # Landau sample
 
+
 ## Sample
 
 Sample N = 50'000 random points following $L(x)$
+
 $$
   L(x) = \frac{1}{\pi} \int \limits_{0}^{+ \infty}
          dt \, e^{-t \ln(t) -xt} \sin (\pi t)
 $$
 
+. . .
+
+gsl_ran_Landau(gsl_rng)
+
 
 ## Compatiblity results:
 
@@ -53,8 +59,85 @@ FWHM:
 
 :::: {.columns}
 :::  {.column width=50%}
-  - $t=0.495$
+  - $t=1.338$
-  - $p=0.620$
+  - $p=0.181$
+:::
+
+:::  {.column width=50%}
+  $$
+  \thus \text{Compatible!}
+  $$
+:::
+::::
+
+
+# Moyal sample
+
+
+## Sample
+
+Sample N = 50'000 random points following $M_{\mu \sigma}(x)$
+
+$$
+  M_{\mu \sigma}(x) = \frac{1}{\sqrt{2 \pi} \sigma} \exp
+         \left[ - \frac{1}{2} \left(
+           \frac{x - \mu}{\sigma}
+           + e^{-\frac{x - \mu}{\sigma}} \right) \right]
+$$
+
+. . .
+
+reverse sampling
+
+- sampling $y$ uniformly in [0, 1] $\quad \longrightarrow \quad x = Q_M(y)$ 
+
+
+## Compatiblity results:
+
+Median:
+
+:::: {.columns}
+:::  {.column width=50%}
+  - $t = 669.940$
+  - $p = 0.000$
+:::
+
+:::  {.column width=50%}
+  $$
+  \thus \text{Not compatible!}
+  $$
+:::
+::::
+
+\vspace{10pt}
+
+. . .
+
+Mode:
+
+:::: {.columns}
+:::  {.column width=50%}
+  - $t = 0.732$
+  - $p = 0.464$
+:::
+
+:::  {.column width=50%}
+  $$
+  \thus \text{Compatible!}
+  $$
+:::
+::::
+
+\vspace{10pt}
+
+. . .
+
+FWHM:
+
+:::: {.columns}
+:::  {.column width=50%}
+  - $t = 1.329$
+  - $p = 0.184$
 :::
 
 :::  {.column width=50%}