From 8ae8a1c7f7c456f77daf825f897039897d181286 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Gi=C3=B9=20Marcer?= <giuliamarcer@yahoo.it>
Date: Thu, 4 Jun 2020 23:20:10 +0200
Subject: [PATCH] slides: create the misc folder

---
 slides/misc/notes_moyal.md | 35 +++++++++++++++++++++++++++++++++++
 slides/misc/todo           | 28 ++++++++++++++++++++++++++++
 2 files changed, 63 insertions(+)
 create mode 100644 slides/misc/notes_moyal.md
 create mode 100644 slides/misc/todo

diff --git a/slides/misc/notes_moyal.md b/slides/misc/notes_moyal.md
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+++ b/slides/misc/notes_moyal.md
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+The Moyal distribution, which  is a steepest descent approximation of the
+Landau distribition, is defines as:
+$$
+  \exp \left( - \frac{x - \mu }{2 \sigma}
+              - \frac{1}{2} \exp \left( - \frac{x -\mu}{\sigma} \right) \right)
+$$
+Mean $m$ and variance $\sigma$:
+$$
+  m = \mu + \sigma [ \gamma + \ln(2) ] \et \sigma = \frac{\pi^2 \sigma^2}{2}
+$$
+Median:
+$$
+  \mu - \sigma \left[ 2 \text{erf}^{-1} \left( \frac{1}{2} \right)^2 \right]
+$$
+skewness and kurtosis are constant:
+$$
+  s = \frac{28 \sqrt{2} Z(3)]{\pi^3} \et k = 7
+$$
+max value:
+$$
+  \frac{1}{\sqrt{2 e \pi}}
+$$
+cdf:
+$$
+  \text{erf} \left( \frac{\exp \left( 
+  - \frac{x - \mu}{2 \sigma} \right)}{\sqrt{2}} \right)
+$$
+
+$\mu$ is the location parameter and $\sigma$ is the scale parameter.  
+The Moyal distribution was first proposed in a 1955 paper by physicist J. E.
+Moyal. The distribution models the energy lost by a fast charged particle
+(and hence the number of ion pairs produced) during ionization. Historically,
+the Moyal distribution has been utilized in the approximation of the Landau
+Distribution and has since found use in modeling a wide array of phenomena.
+
diff --git a/slides/misc/todo b/slides/misc/todo
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index 0000000..70ce2c0
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+++ b/slides/misc/todo
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+produrre moyal più simile possibile alla Landau e poi distinguiamole.
+renderle simili:
+  stessa moda
+  stessa fwhm
+  stessa mediana
+poi applichiamo i quattro test che abbiamo implementato per distinguerle.
+guardare anche quanti punti stanno oltre un certo numero di sigma.
+
+Slide  1: Obiettivo (comfronto e identificazione pdf corretta)
+Slide  2: Landau / Moyal (cosa sono)
+Slide  3: Landau patologica
+Slide  4: Landau mediana attesa
+Slide  5: Landau moda attesa
+Slide  6: Landau FWHM attesa
+Slide  7: Moyal non patologica
+Slide  8: Moyal mediana attesa
+Slide  9: Moyal moda attesa
+Slide 10: Moyal FWHM attesa
+Slide 11: Campione generato
+Slide 12: Spessore code
+Slide 13: Misura punti estremi
+Slide 14: Relativi risultati
+Slide 15: KS (a cosa serve)
+Slide 16: KS (come funziona 1)
+Slide 17: KS (come funziona 2)
+Slide 18: Relativi risultati
+Slide 19: Conclusioni
+Slide 20: