94 lines
1.5 KiB
Markdown
94 lines
1.5 KiB
Markdown
# Goal
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## Goal
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- Generate a sample $L$ of points from a Landau PDF
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- Generate a sample $M$ of points from a Moyal PDF
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. . .
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- Implement a bunch of statistical tests
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. . .
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- Check if they work:
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- the sample $L$ truly comes from a Landau PDF
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- the sample $M$ does not come from a Landau PDF
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## Why?
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The Landau and Moyal PDFs are really similar. Historically, the latter was
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utilized in the approximation of the former.
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:::: {.columns}
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::: {.column width=33%}
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{height=130pt}
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:::
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::: {.column width=33%}
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{height=130pt}
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:::
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::: {.column width=33%}
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{height=130pt}
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:::
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::::
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## Two similar distributions
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:::: {.columns}
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::: {.column width=50%}
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Landau PDF
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$$
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L(x) = \frac{1}{\pi} \int \limits_{0}^{+ \infty}
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dt \, e^{-t \ln(t) -xt} \sin (\pi t)
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$$
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:::
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::: {.column width=50%}
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Moyal PDF
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$$
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M(x) = \frac{1}{\sqrt{2 \pi}} \exp \left[ - \frac{1}{2}
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\left( x + e^{- x} \right) \right]
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$$
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:::
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::::
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\vspace{10pt}
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:::: {.columns}
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::: {.column width=50%}
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:::
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::: {.column width=50%}
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:::
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::::
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## Two similar distributions
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## Statistical tests
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. . .
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- Parameters comparison:
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- compatibility between expected and observed PDF parameters
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. . .
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- Kolmogorov - Smirnov:
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- compatibility between expected and observed CDF
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. . .
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- Trapani test:
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- compatibiity between expected and observed mean
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