265 lines
2.8 KiB
Markdown
265 lines
2.8 KiB
Markdown
# Landau sample
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## Sample
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Sample N = 50'000 random points following $L(x)$
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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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gsl_ran_Landau(gsl_rng)
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## Compatibility results:
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Median:
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:::: {.columns}
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::: {.column width=50%}
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- $t = 0.761$
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- $p = 0.446$
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:::
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::: {.column width=50%}
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$$
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\hence \text{Compatible!}
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$$
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:::
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::::
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\vspace{10pt}
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. . .
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Mode:
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:::: {.columns}
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::: {.column width=50%}
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- $t = 1.012$
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- $p = 0.311$
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:::
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::: {.column width=50%}
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$$
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\hence \text{Compatible!}
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$$
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:::
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::::
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\vspace{10pt}
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. . .
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FWHM:
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:::: {.columns}
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::: {.column width=50%}
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- $t=1.338$
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- $p=0.181$
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:::
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::: {.column width=50%}
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$$
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\hence \text{Compatible!}
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$$
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:::
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::::
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# Moyal sample
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## Sample
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Sample N = 50'000 random points following $M_{\mu \sigma}(x)$
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$$
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M_{\mu \sigma}(x) = \frac{1}{\sqrt{2 \pi} \sigma} \exp
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\left[ - \frac{1}{2} \left(
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\frac{x - \mu}{\sigma}
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+ e^{-\frac{x - \mu}{\sigma}} \right) \right]
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$$
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. . .
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reverse sampling
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- sampling $y$ uniformly in [0, 1] $\hence x = Q_M(y)$
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## Compatibility results:
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Median:
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:::: {.columns}
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::: {.column width=50%}
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- $t = 669.940$
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- $p = 0.000$
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:::
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::: {.column width=50%}
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$$
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\hence \text{Not compatible!}
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$$
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:::
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::::
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\vspace{10pt}
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. . .
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Mode:
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:::: {.columns}
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::: {.column width=50%}
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- $t = 0.732$
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- $p = 0.464$
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:::
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::: {.column width=50%}
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$$
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\hence \text{Compatible!}
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$$
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:::
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::::
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\vspace{10pt}
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. . .
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FWHM:
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:::: {.columns}
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::: {.column width=50%}
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- $t = 1.329$
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- $p = 0.184$
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:::
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::: {.column width=50%}
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$$
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\hence \text{Compatible!}
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$$
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:::
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::::
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# KS results
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## Samples results
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$N = 50000$ sampled points
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. . .
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Landau sample:
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:::: {.columns}
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::: {.column width=50%}
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- $D = 0.004$
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- $p = 0.379$
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:::
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::: {.column width=50%}
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$$
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\hence \text{Compatible!}
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$$
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:::
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::::
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\vspace{10pt}
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. . .
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Moyal sample:
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:::: {.columns}
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::: {.column width=50%}
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- $D = 0.153$
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- $p = 0.000$
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:::
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::: {.column width=50%}
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$$
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\hence \text{Not compatible!}
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$$
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:::
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::::
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# Trapani results
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## Samples results
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. . .
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Landau sample:
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:::: {.columns}
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::: {.column width=33%}
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$$
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\mu_1
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\begin{cases}
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\Theta = 0.255 \\
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p = 0.614
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\end{cases}
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$$
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:::
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::: {.column width=33% .c}
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$$
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\mu_2
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\begin{cases}
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\Theta = 0.432 \\
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p = 0.511
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\end{cases}
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$$
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:::
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::: {.column width=33% .c}
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$$
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\hence \text{Infinite!}
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$$
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:::
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::::
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. . .
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\vspace{20pt}
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Moyal sample:
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:::: {.columns}
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::: {.column width=33%}
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$$
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\mu_1
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\begin{cases}
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\Theta^2 = 106 \\
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p = 0.000
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\end{cases}
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$$
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:::
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::: {.column width=33%}
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$$
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\mu_2
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\begin{cases}
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\Theta^2 = 162 \\
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p = 0.000
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\end{cases}
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$$
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:::
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::: {.column width=33% .c}
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$$
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\hence \text{Finite!}
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$$
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:::
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::::
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