1.2 KiB
1.2 KiB
Goal
Goal
What?
- Generate a sample of points from a Moyal PDF
- Prove it truly comes from it and not from a Landau PDF
How?
- Applying some hypothesis testings
Why?
The Landau and Moyal PDFs are really similar. Historically, the latter distribution was utilized in the approximation of the Landau Distribution.
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Two similar distributions
:::: {.columns .c} ::: {.column width=50%} \begin{center} Landau PDF
$$
L(x) = \frac{1}{\pi} \int \limits_{0}^{+ \infty}
dt \, e^{-t \ln(t) -xt} \sin (\pi t)
\end{center} ::: ::: {.column width=50%} \begin{center} Moyal PDF
$$
M(x) = \frac{1}{\sqrt{2 \pi}} \exp \left[ - \frac{1}{2}
\left( x + e^{- x} \right) \right]
\end{center} ::: ::::
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::: {.column width=50%}
Two similar distributions
\centering
