69 lines
1.1 KiB
Markdown
69 lines
1.1 KiB
Markdown
# Goal
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## Goal
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What?
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- Generate a sample of points from a Moyal PDF
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- Prove it truly comes from it and not from a Landau PDF
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How?
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- Applying some hypothesis testings
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## Why?
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The Landau and Moyal PDFs are really similar. Historically, the latter distribution was utilized in
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the approximation of the Landau Distribution.
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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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:::: {.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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