From 68ae4680ffeaa3d84fd0b32467b61f8098e771d6 Mon Sep 17 00:00:00 2001
From: Joel Kronqvist <joel.kronqvist@iki.fi>
Date: Mon, 8 Jun 2026 11:41:41 +0300
Subject: added plots & equations for EV distribs

---
 main.org | 97 +++++++++++++++++++++++++++++++++++++++++++++++++---------------
 1 file changed, 74 insertions(+), 23 deletions(-)

diff --git a/main.org b/main.org
index b940e2e..071aaa0 100644
--- a/main.org
+++ b/main.org
@@ -1,6 +1,7 @@
-#+TITLE: Formalizing the Classification of Extreme Value Distributions
-#+SUBTITLE: One-parameter subgroups of Affine transformations
+#+TITLE: Ääriarvojakaumien luokittelun formalisointi
+#+SUBTITLE: Affiinit reaaliakselin muunnokset
 #+AUTHOR: Joel Kronqvist
+#+LANGUAGE: fi
 #+startup: beamer
 #+LaTeX_CLASS: beamer
 #+LaTeX_CLASS_OPTIONS: [bigger]
@@ -8,12 +9,13 @@
 #+LATEX_HEADER: \usepackage{fontspec}
 #+LaTeX_HEADER: \setmonofont[Scale=0.8]{DejaVu Sans Mono}
 #+LaTeX_HEADER: \usetheme{Copenhagen}
+#+LaTeX_HEADER: \usepackage[finnish]{babel}
+#+LaTeX_HEADER: \newcommand{\R}{\mathbb{R}}
+#+LaTeX_HEADER: \renewcommand{\vec}[1]{\mathbf{#1}}
 
+* Formalisointi
 
-
-* Formalization
-
-** First slide of formalization
+** Esimerkki
 
 *** Text                                                              :BMCOL:
 :PROPERTIES:
@@ -30,7 +32,6 @@ Sample text
 :BEAMER_col: .6
 :END:
 
-
 #+NAME: leanexample
 #+begin_src lean4
     variable (p q : Prop)
@@ -42,35 +43,85 @@ Sample text
         And.intro hq hp
 #+end_src
 
-  
-#     \begin{minted}[autogobble, bgcolor=codebg, fontsize=\footnotesize, bgcolorpadding=2pt]{lean4}
 
-* Extreme value distributions
+* Ääriarvojakaumat
+
+** Mitä ne ovat?
+
+Matikkaselitystä
+
+
+** Kertymäfunktiot
+
+
+\begin{align*}
+  \Phi_\alpha (x) &:= \begin{cases}
+    0, & \text{kun}\ x \le 0, \\
+    \exp( -x^{-\alpha}), &\text{muutoin}, \\
+  \end{cases} \\
+  \Psi_\alpha (x) &:= \begin{cases}
+    \exp(-(-x)^\alpha), & \text{kun}\ x \le 0, \\
+    1, &\text{muutoin}, \\
+  \end{cases} \\
+  \Lambda(x) &:= \exp(-e^{-x}), x \in \R
+\end{align*}
 
-** Fréchet
+
+** Kuvaajat
 
 #+name: plot-frechet
-#+begin_src python :results file link :file "frechet-plot.png" :exports results
+#+begin_src python :results output :file ./plot.png :exports results
   import numpy as np
   import matplotlib.pyplot as plt
-  a = 2.0 # α > 0  (shape/dispersion parameter)
-  x = np.linspace(1e-6, 5, 500)
-  pdf = np.vectorize(lambda x: a*x**(-a-1)*np.exp(-x**(-a)) if x > 0 else 0)(x)
-  plt.plot(x, pdf, lw=2, color='steelblue')
-  plt.savefig('frechet-plot.png')
+
+  fig, axes = plt.subplots(1, 3)
+  fig.set_size_inches(10, 4)
+
+  a1 = 3.0
+  a2 = 1.2
+
+  pl = lambda axi, x, f, lab: axes[axi].plot(x, np.vectorize(f)(x), label=lab)
+
+  pl(
+      0,
+      np.linspace(1e-6, 3, 500),
+      lambda x: a1*x**(-a1-1)*np.exp(-(x**(-a1))) if x > 0 else 0,
+      "$ \\frac{\\mathrm{d}}{\\mathrm{d} x} \\Phi_\\alpha (x) $"
+  )
+
+  pl(
+      1,
+      np.linspace(-3, 1, 500),
+      lambda x: a2 * ((-x) ** (a2 - 1)) * np.exp(-1 * ((-x) ** a2)) if x < 0 else 0,
+      "$ \\frac{\\mathrm{d}}{\\mathrm{d} x} \\Psi_\\alpha (x) $"
+  )
+
+  pl(
+      2,
+      np.linspace(-5, 5, 500),
+      lambda x: np.exp(-x) * np.exp(-np.exp(-x)),
+      "$ \\frac{\\mathrm{d}}{\\mathrm{d} x} \\Lambda (x) $"
+  )
+
+  for ax in axes:
+      ax.legend()
+
+  plt.savefig('plot.png')
 #+end_src
 
 #+RESULTS: plot-frechet
-[[file:frechet-plot.png]]
 
-** Gumbel
+#+ATTR_LATEX: :width 1.1\textwidth
+#+CAPTION: Test caption
+[[./plot.png]]
 
-** Weibull
 
+* Affiinit muunnokset
 
-* Affine transformations
+** Dia 1
 
-** This is slide 1 on affine transformations
+Teksti 1
 
-Maybe add several slides to each category?
 
+* TODO
+** Nimi?
-- 
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