slides: slim down a few slides

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Michele Guerini Rocco 2020-07-08 09:50:07 +02:00
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## Goal
Construct six statistical tests to assert whether a sample comes from a Landau
distribution
Test whether sample comes from a Landau distribution
. . .
- Generate a sample $L$ from a Landau PDF
- Generate a sample $M$ from a Moyal PDF
- sample $L$ from Landau PDF
- sample $M$ from Moyal PDF
. . .
$H_0$: sample following Landau PDF
$H_0$: sample from Landau PDF
- can we accept $H_0$ for $L$?
- can we reject $H_0$ for $M$?
- accept $H_0$ for $L$?
- reject $H_0$ for $M$?
## Why Moyal?
The Landau and Moyal PDFs are really similar.
Historically, the latter was utilized as an approximation of the former.
Landau and Moyal PDFs are similar
```{=latex}
\includegraphics<1>[height=5.5cm]{images/moyal-photo.jpg}

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- $F(x)$ is the expected CDF
- $F_N(x)$ is the empirical CDF
- sort points in ascending order
- number of points preceding the point normalized by $N$
. . .