diff --git a/slides/sections/4.md b/slides/sections/4.md index c61e48e..eb38174 100644 --- a/slides/sections/4.md +++ b/slides/sections/4.md @@ -71,7 +71,7 @@ $$ f_\varepsilon(x) = \frac{1}{N\varepsilon} \sum_{i = 1}^N G \left( \frac{x-x_i}{\varepsilon} \right) \with - \varepsilon = 0.63 \, S_N + \varepsilon = 0.88 \, S_N \left( \frac{d + 2}{4}N \right)^{-1/(d + 4)} $$ diff --git a/slides/sections/6.md b/slides/sections/6.md index 19117c0..3aff8a7 100644 --- a/slides/sections/6.md +++ b/slides/sections/6.md @@ -1,13 +1,19 @@ # Landau sample + ## Sample Sample N = 50'000 random points following $L(x)$ + $$ L(x) = \frac{1}{\pi} \int \limits_{0}^{+ \infty} dt \, e^{-t \ln(t) -xt} \sin (\pi t) $$ +. . . + +gsl_ran_Landau(gsl_rng) + ## Compatiblity results: @@ -53,8 +59,85 @@ FWHM: :::: {.columns} ::: {.column width=50%} - - $t=0.495$ - - $p=0.620$ + - $t=1.338$ + - $p=0.181$ +::: + +::: {.column width=50%} + $$ + \thus \text{Compatible!} + $$ +::: +:::: + + +# Moyal sample + + +## Sample + +Sample N = 50'000 random points following $M_{\mu \sigma}(x)$ + +$$ + M_{\mu \sigma}(x) = \frac{1}{\sqrt{2 \pi} \sigma} \exp + \left[ - \frac{1}{2} \left( + \frac{x - \mu}{\sigma} + + e^{-\frac{x - \mu}{\sigma}} \right) \right] +$$ + +. . . + +reverse sampling + +- sampling $y$ uniformly in [0, 1] $\quad \longrightarrow \quad x = Q_M(y)$ + + +## Compatiblity results: + +Median: + +:::: {.columns} +::: {.column width=50%} + - $t = 669.940$ + - $p = 0.000$ +::: + +::: {.column width=50%} + $$ + \thus \text{Not compatible!} + $$ +::: +:::: + +\vspace{10pt} + +. . . + +Mode: + +:::: {.columns} +::: {.column width=50%} + - $t = 0.732$ + - $p = 0.464$ +::: + +::: {.column width=50%} + $$ + \thus \text{Compatible!} + $$ +::: +:::: + +\vspace{10pt} + +. . . + +FWHM: + +:::: {.columns} +::: {.column width=50%} + - $t = 1.329$ + - $p = 0.184$ ::: ::: {.column width=50%}