diff --git a/slides/sections/8.md b/slides/sections/8.md index d4b00d3..900f4a1 100644 --- a/slides/sections/8.md +++ b/slides/sections/8.md @@ -59,223 +59,90 @@ $$ \setbeamercovered{transparent} -## Landau results: +## Landau sample results -Median: - -:::: {.columns} -::: {.column width=50%} - - $t = 0.761$ - - $p = 0.446$ -::: - -::: {.column width=50%} - $$ - \hence \text{Compatible!} - $$ -::: -:::: - -\vspace{10pt} - -. . . - -Mode: - -:::: {.columns} -::: {.column width=50%} - - $t = 1.012$ - - $p = 0.311$ -::: - -::: {.column width=50%} - $$ - \hence \text{Compatible!} - $$ -::: -:::: - -\vspace{10pt} - -. . . - -FWHM: - -:::: {.columns} -::: {.column width=50%} - - $t=1.338$ - - $p=0.181$ -::: - -::: {.column width=50%} - $$ - \hence \text{Compatible!} - $$ -::: -:::: +```{=latex} +\begin{center} +\begin{tabular}{rcccc} + \toprule + & & median & mode & fwhm \\ + \midrule + \multirow{2}{*}{50000} & t & 0.761 & 1.012 & 1.338 \\ + & p & \gre{0.446} & \gre{0.311} & \gre{0.181} \\ + \midrule + \multirow{2}{*}{1000} & t & 1.549 & 0.072 & 3.790 \\ + & p & \gre{0.121} & \gre{0.943} & \red{0.000} \\ + \midrule + \multirow{2}{*}{200} & t & 2.508 & 0.418 & 1.547 \\ + & p & \red{0.012} & \gre{0.676} & \gre{0.122} \\ + \toprule +\end{tabular} +\end{center} +``` -## Moyal results: +## Moyal sample results -Median: - -:::: {.columns} -::: {.column width=50%} - - $t = 669.940$ - - $p = 0.000$ -::: - -::: {.column width=50%} - $$ - \hence \text{Not compatible!} - $$ -::: -:::: - -\vspace{10pt} - -. . . - -Mode: - -:::: {.columns} -::: {.column width=50%} - - $t = 0.732$ - - $p = 0.464$ -::: - -::: {.column width=50%} - $$ - \hence \text{Compatible!} - $$ -::: -:::: - -\vspace{10pt} - -. . . - -FWHM: - -:::: {.columns} -::: {.column width=50%} - - $t = 1.329$ - - $p = 0.184$ -::: - -::: {.column width=50%} - $$ - \hence \text{Compatible!} - $$ -::: -:::: +```{=latex} +\begin{center} +\begin{tabular}{rcccc} + \toprule + & & median & mode & fwhm \\ + \midrule + \multirow{2}{*}{50000} & t & 669.9 & 0.732 & 1.329 \\ + & p & \gre{0.000} & \gre{0.464} & \gre{0.184} \\ + \midrule + \multirow{2}{*}{1000} & t & 25.47 & 0.665 & 1.890 \\ + & p & \gre{0.000} & \gre{0.506} & \gre{0.059} \\ + \midrule + \multirow{2}{*}{200} & t & 48.12 & 0.028 & 0.388 \\ + & p & \gre{0.000} & \gre{0.978} & \gre{0.698} \\ + \toprule +\end{tabular} +\end{center} +``` -## KS results +## KS samples results -$N = 50000$ sampled points - -. . . - -Landau sample: - -:::: {.columns} -::: {.column width=50%} - - $D = 0.004$ - - $p = 0.379$ -::: - -::: {.column width=50%} - $$ - \hence \text{Compatible!} - $$ -::: -:::: - -\vspace{10pt} - -. . . - -Moyal sample: - -:::: {.columns} -::: {.column width=50%} - - $D = 0.153$ - - $p = 0.000$ -::: - -::: {.column width=50%} - $$ - \hence \text{Not compatible!} - $$ -::: -:::: +```{=latex} +\begin{center} +\begin{tabular}{rlll} + \toprule + & & L sample & M sample \\ + \midrule + \multirow{2}{*}{50000} & D & 0.004 & 0.153 \\ + & p & \gre{0.379} & \gre{0.000} \\ + \midrule + \multirow{2}{*}{1000} & D & 0.020 & 0.162 \\ + & p & \gre{0.794} & \gre{0.000} \\ + \midrule + \multirow{2}{*}{200} & D & 0.086 & 0.226 \\ + & p & \gre{0.100} & \gre{0.000} \\ + \toprule +\end{tabular} +\end{center} +``` -## Trapani results +## Trapani samples results -. . . - -Landau sample: - -:::: {.columns} -::: {.column width=33%} - $$ - \mu_1 - \begin{cases} - \Theta = 0.255 \\ - p = 0.614 - \end{cases} - $$ -::: - -::: {.column width=33% .c} - $$ - \mu_2 - \begin{cases} - \Theta = 0.432 \\ - p = 0.511 - \end{cases} - $$ -::: - -::: {.column width=33% .c} - $$ - \hence \text{Infinite!} - $$ -::: -:::: - -. . . - -\vspace{20pt} - -Moyal sample: - -:::: {.columns} -::: {.column width=33%} - $$ - \mu_1 - \begin{cases} - \Theta^2 = 106 \\ - p = 0.000 - \end{cases} - $$ -::: - -::: {.column width=33%} - $$ - \mu_2 - \begin{cases} - \Theta^2 = 162 \\ - p = 0.000 - \end{cases} - $$ -::: - -::: {.column width=33% .c} - $$ - \hence \text{Finite!} - $$ -::: -:::: +```{=latex} +\begin{center} +\begin{tabular}{rlllll} + \toprule + & & \multicolumn{2}{c}{L sample} & \multicolumn{2}{c}{M sample} \\ + & & mean & variance & mean & variance \\ + \midrule + \multirow{2}{*}{50000} & $\Theta$ & 0.255 & 0.432 & 161.1 & 162.5 \\ + & p & \gre{0.614} & \gre{0.511} & \gre{0.000} & \gre{0.000} \\ + \midrule + \multirow{2}{*}{1000} & $\Theta$ & 0.809 & 0.809 & 10.83 & 5.823 \\ + & p & \gre{0.368} & \gre{0.368} & \gre{0.016} & \gre{0.001} \\ + \midrule + \multirow{2}{*}{200} & $\Theta$ & 0.472 & 0.170 & 2.232 & 2.981 \\ + & p & \gre{0.492} & \gre{0.680} & \red{0.135} & \red{0.084} \\ + \toprule +\end{tabular} +\end{center} +```