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| -rw-r--r-- | main.org | 97 |
1 files changed, 74 insertions, 23 deletions
@@ -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? |