sections: fix and add a lot of things

slides/sections/2.md

@@ -1,4 +1,4 @@
-# Landau PDF
+# Landau distribution
 
 
 ## Landau PDF
@@ -9,6 +9,13 @@
     L(x) = \frac{1}{\pi} \int \limits_{0}^{+ \infty}
            dt \, e^{-t \ln(t) -xt} \sin (\pi t)
   $$
+
+  . . .
+
+  \vspace{30pt}
+
+  \centering
+  No closed form for \textcolor{cyclamen}{ANYTHING}
 :::
 
 :::  {.column width=50%}
@@ -16,10 +23,6 @@
 :::
 ::::
 
-. . .
-
-No closed form for \textcolor{cyclamen}{ANYTHING}
-
 
 ## Landau median
 

slides/sections/4.md

@@ -64,16 +64,16 @@ Half Sample Mode
   \draw [line width=3, ->, cyclamen] (-5,0) -- (5,0);
   \node [right] at (5,0) {$x$};
   % points
-  \draw [blue, fill=blue] (-4.6,-0.1) rectangle (-4.8,0.1);
+  \draw [blue!50!black, fill=blue] (-4.6,-0.1) rectangle (-4.8,0.1);
-  \draw [blue, fill=blue] (-4,-0.1)   rectangle (-4.2,0.1);
+  \draw [blue!50!black, fill=blue] (-4,-0.1)   rectangle (-4.2,0.1);
-  \draw [blue, fill=blue] (-3.3,-0.1) rectangle (-3.5,0.1);
+  \draw [blue!50!black, fill=blue] (-3.3,-0.1) rectangle (-3.5,0.1);
-  \draw [blue, fill=blue] (-2.3,-0.1) rectangle (-2.5,0.1);
+  \draw [blue!50!black, fill=blue] (-2.3,-0.1) rectangle (-2.5,0.1);
-  \draw [blue, fill=blue] (-0.6,-0.1) rectangle (-0.8,0.1);
+  \draw [blue!50!black, fill=blue] (-0.6,-0.1) rectangle (-0.8,0.1);
-  \draw [blue, fill=blue] (-0.1,-0.1) rectangle (0.1,0.1);
+  \draw [blue!50!black, fill=blue] (-0.1,-0.1) rectangle (0.1,0.1);
-  \draw [blue, fill=blue] (1.1,-0.1)  rectangle (1.3,0.1);
+  \draw [blue!50!black, fill=blue] (1.1,-0.1)  rectangle (1.3,0.1);
-  \draw [blue, fill=blue] (2  ,-0.1)  rectangle (2.2,0.1);
+  \draw [blue!50!black, fill=blue] (2  ,-0.1)  rectangle (2.2,0.1);
-  \draw [blue, fill=blue] (2.7,-0.1)  rectangle (2.9,0.1);
+  \draw [blue!50!black, fill=blue] (2.7,-0.1)  rectangle (2.9,0.1);
-  \draw [blue, fill=blue] (4,-0.1)    rectangle (4.2,0.1);
+  \draw [blue!50!black, fill=blue] (4,-0.1)    rectangle (4.2,0.1);
   % future nodes
   \node at (-1,-0.3)  (1a) {};
   \node at (3.1,0.3)  (1b) {};
@@ -131,7 +131,7 @@ $$
 \setbeamercovered{transparent}
 . . .
 
-Kernel Density Estimation
+**Kernel Density Estimation**
 
 :::: {.columns}
 :::  {.column width=50% .c}
@@ -150,10 +150,10 @@ Kernel Density Estimation
   \begin{center}
   \begin{tikzpicture}
     % points
-    \draw [blue, fill=blue] (-2,-0.1) rectangle (-1.8,0.1);
+    \draw [blue!50!black, fill=blue] (-2,-0.1) rectangle (-1.8,0.1);
-    \draw [blue, fill=blue] (-0.1,-0.1) rectangle (0.1,0.1);
+    \draw [blue!50!black, fill=blue] (-0.1,-0.1) rectangle (0.1,0.1);
-    \draw [blue, fill=blue] (1.3,-0.1) rectangle (1.5,0.1);
+    \draw [blue!50!black, fill=blue] (1.3,-0.1) rectangle (1.5,0.1);
-    \draw [blue, fill=blue] (0.7,-0.1) rectangle (0.9,0.1);
+    \draw [blue!50!black, fill=blue] (0.7,-0.1) rectangle (0.9,0.1);
     \pause
     % lines
     \draw [cyclamen, dashed] (-1.9,0.1) -- (-1.9,1);

slides/sections/5.md

@@ -1,4 +1,4 @@
-# Kolmogorov - Smirnov test
+# Kolmogorov-Smirnov test
 
 
 ## KS
@@ -7,16 +7,61 @@ Quantify distance between expected and observed CDF
 
 . . .
 
-KS statistic:
+:::: {.columns}
+:::  {.column width=50% .c}
+  KS statistic:
 
-$$
+  $$
-  D_N = \text{sup}_x |F_N(x) - F(x)|
+    D_N = \text{sup}_x |F_N(x) - F(x)|
-$$
+  $$
 
-- $F(x)$ is the expected CDF
+  \vspace{20pt}
-- $F_N(x)$ is the empirical CDF of $N$ sampled points
+
-  - sort points in ascending order
+  - $F(x)$ is the expected CDF
-  - number of points preceding the point normalized by $N$
+  - $F_N(x)$ is the empirical CDF
+    - sort points in ascending order
+    - number of points preceding the point normalized by $N$
+
+:::
+
+:::  {.column width=50%}
+  \setbeamercovered{}
+  \begin{center}
+  \begin{tikzpicture}
+    % axes
+    \draw [thick, ->] (-2.5,0) -- (0,0) -- (0,4.5);
+    \draw [thick, ->] (0,0) -- (2.5,0);
+    % empiric
+    \draw [cyclamen, fill=cyclamen!20!white] (-2.5,0) rectangle (-1.5,0.5);
+    \draw [cyclamen, fill=cyclamen!20!white] (-1.5,0) rectangle (-0.9,1);
+    \draw [cyclamen, fill=cyclamen!20!white] (-0.9,0) rectangle (-0.6,1.5);
+    \draw [cyclamen, fill=cyclamen!20!white] (-0.6,0) rectangle ( 0.2,2);
+    \draw [cyclamen, fill=cyclamen!20!white] ( 0.2,0) rectangle ( 0.5,2.5);
+    \draw [cyclamen, fill=cyclamen!20!white] ( 0.5,0) rectangle ( 0.8,3);
+    \draw [cyclamen, fill=cyclamen!20!white] ( 0.8,0) rectangle ( 1.6,3.5);
+    \draw [cyclamen, fill=cyclamen!20!white] ( 1.6,0) rectangle ( 2.3,4);
+    \draw [cyclamen, fill=cyclamen!20!white] ( 2.3,0) rectangle ( 2.5,4.5);
+    % points
+    \draw [blue!50!black, fill=blue] (-2.6,-0.1) rectangle (-2.4,0.1); %-2.5
+    \draw [blue!50!black, fill=blue] (-1.6,-0.1) rectangle (-1.4,0.1); %-1.5
+    \draw [blue!50!black, fill=blue] (-1,-0.1)   rectangle (-0.8,0.1); %-0.9
+    \draw [blue!50!black, fill=blue] (-0.7,-0.1) rectangle (-0.5,0.1); %-0.6
+    \draw [blue!50!black, fill=blue] (0.1,-0.1)  rectangle (0.3,0.1);  % 0.2
+    \draw [blue!50!black, fill=blue] (0.4,-0.1)  rectangle (0.6,0.1);  % 0.5
+    \draw [blue!50!black, fill=blue] (0.7,-0.1)  rectangle (0.9,0.1);  % 0.8
+    \draw [blue!50!black, fill=blue] (1.5,-0.1)  rectangle (1.7,0.1);  % 1.6
+    \draw [blue!50!black, fill=blue] (2.2,-0.1)  rectangle (2.4,0.1);  % 2.3
+    % expected
+    \pause
+    \draw[domain=-2.5:2.5, yscale=5, smooth, variable=\x, blue, very thick]
+          plot ({\x}, {((atan(\x)*pi/180) + pi/2)/pi});
+    \pause
+    \draw [very thick, cyclamen] (0.8,3.6) -- (0.8,4.05);
+  \end{tikzpicture}
+  \end{center}
+  \setbeamercovered{transparent}
+:::
+::::
 
 
 ## KS