7.2 KiB
Results
Compatibility test
Comparing sample properties:
p = 1 - \text{erf} \left( \frac{t}{\sqrt{2}} \right)\ \with
t = \frac{|x\ex - x\ob|}{\sqrt{\sigma\ex^2 + \sigma\ob^2}}
x\exandx\obare the expected and observed values\sigma\exand\sigma\obare their absolute errors
. . .
At 95% confidence level, the values are compatible if:
p > 0.05
Compatibility test
\setbeamercovered{} \begin{center} \begin{tikzpicture}[>=Stealth] %notes \draw [very thick, gray] (0,0) -- (0,3); \draw [very thick, gray] (-1.45,1.5) -- (1.45,1.5); \draw [very thick, gray] (-1.35,1.3) -- (-1.55,1.7); \draw [very thick, gray] ( 1.35,1.3) -- ( 1.55,1.7); \node at (0,-0.4) {$x\ex$}; \node [right] at (1.7,1.7) {$2 , \sqrt{\sigma\ex^2 + \sigma\ob^2}$}; % axes \draw [very thick, <->] (-5,4) -- (-5,0) -- (5,0); \node [right] at (5,0) {$x$}; % Gaussian \draw [domain=-5:5, smooth, variable=\x, cyclamen, very thick] plot ({\x}, {3exp(-(\x\x/3))}); \pause % area \fill [domain=2:5, smooth, variable=\x, cyclamen!20!white, very thick] (2,0) -- plot ({\x}, {3exp(-(\x\x/3))}) -- (5,0) -- cycle; \fill [domain=-5:-2, smooth, variable=\x, cyclamen!20!white, very thick] (-5,0) -- plot ({\x}, {3exp(-(\x\x/3))}) -- (-2,0) -- cycle; % axes \draw [very thick, <->] (-5,4) -- (-5,0) -- (5,0); % Gaussian \draw [domain=-5:5, smooth, variable=\x, cyclamen, very thick] plot ({\x}, {3exp(-(\x\x/3))}); %notes \draw [thick, cyclamen] (-2,0) -- (-2,0.8); \draw [thick, cyclamen] ( 2,0) -- ( 2,0.8); \node at (2,-0.4) {$x\ob$}; \end{tikzpicture} \end{center} \setbeamercovered{transparent}
L sample results
\vspace{20pt}
\begin{center}
\begin{tabular}{rcccc}
\toprule
& & median & mode & fwhm \
\midrule
\multirow{2}{}{50000} & t & 0.027 & 1.012 & 1.338 \
& p & \gre{0.979} & \gre{0.311} & \gre{0.181} \
\midrule
\multirow{2}{}{5000} & t & 0.912 & 0.200 & 3.033 \
& p & \gre{0.362} & \gre{0.841} & \red{0.002} \
\midrule
\multirow{2}{*}{1000} & t & 1.189 & 0.232 & 0.208 \
& p & \gre{0.235} & \gre{0.817} & \gre{0.835} \
\toprule
\end{tabular}
\end{center}
\setbeamercovered{} \begin{center} \begin{tikzpicture}[>=Stealth, overlay] % Rectangles \draw <2> [gray, very thick] (-1.4,0.3) rectangle (0.4,5.5); \draw <3> [gray, very thick] (0.4,0.3) rectangle (2,5.5); \draw <4> [gray, very thick] (2,0.3) rectangle (3.8,5.5); % Estimations ellipses \draw <5-> [cyclamen, thick] (2.8,3.57) ellipse (0.8cm and 0.3cm); \draw <5-> [cyclamen, thick] (2.8,2.18) ellipse (0.8cm and 0.3cm); \draw <5-> [cyclamen, thick] (2.8,0.8) ellipse (0.8cm and 0.3cm); % Estimations notes \draw <6> [fill=white] (-5.5,-0.1) rectangle (0.3,2.3); \node <6> [above right, align=right] at (-5.5,-0.1) { $w\ex = 4.02... \hspace{22pt} $\ $50000 \hence w\ob = 4.11 \pm 0.07$\ $5000 \hence w\ob = 4.40 \pm 0.13$\ $1000 \hence w\ob = 3.96 \pm 0.27$}; % FHWM notes \draw <7-> [fill=white] (-5.5,2.9) rectangle (-1.4,5.1); \node <7-> [above right, align=center] at (-5.5,3) { $f_\varepsilon(x) = \frac{1}{N\varepsilon} \sum_{i = 1}^N G \left( \frac{x-x_i}{\varepsilon} \right)$\\ $\varepsilon = 0.88 , S_N \left( \frac{d + 2}{4}N \right)^{-1/(d + 4)}$}; \draw <8> [cyclamen, thick] (-4.45,3.45) ellipse (0.4cm and 0.3cm); \end{tikzpicture} \end{center} \setbeamercovered{transparent}
M sample results
\vspace{20pt}
\begin{center}
\begin{tabular}{rcccc}
\toprule
& & median & mode & fwhm \
\midrule
\multirow{2}{}{50000} & t & 58.01 & 0.732 & 1.329 \
& p & \gre{0.000} & \gre{0.464} & \gre{0.184} \
\midrule
\multirow{2}{}{5000} & t & 16.80 & 0.014 & 0.215 \
& p & \gre{0.000} & \gre{0.989} & \gre{0.830} \
\midrule
\multirow{2}{*}{1000} & t & 11.61 & 0.028 & 1.001 \
& p & \gre{0.000} & \gre{0.978} & \gre{0.317} \
\toprule
\end{tabular}
\end{center}
\setbeamercovered{} \begin{center} \begin{tikzpicture}[>=Stealth, overlay] % Rectangles \draw <2> [gray, very thick] (-1.4,0.3) rectangle (0.4,5.5); \draw <3> [gray, very thick] (0.4,0.3) rectangle (2,5.5); \draw <4,5,6> [gray, very thick] (2,0.3) rectangle (3.8,5.5); \node <5> at (-2,2.5) {\includegraphics{images/gamo-pdf.pdf}}; \node <6> at (-2,2.5) {\includegraphics{images/gala-pdf.pdf}}; \draw <5,6> [thick] (-5.15,0) rectangle (1.22,5.05); \end{tikzpicture} \end{center} \setbeamercovered{transparent}
KS samples results
\vspace{10pt}
\begin{center}
\begin{tabular}{rccc}
\toprule
& & L sample & M sample \
\midrule
\multirow{2}{}{50000} & D & 0.004 & 0.153 \
& p & \gre{0.379} & \gre{0.000} \
\midrule
\multirow{2}{}{5000} & D & 0.010 & 0.148 \
& p & \gre{0.714} & \gre{0.000} \
\midrule
\multirow{2}{}{1000} & D & 0.026 & 0.162 \
& p & \gre{0.478} & \gre{0.000} \
\midrule
\multirow{2}{}{200} & D & 0.054 & 0.205 \
& p & \gre{0.579} & \gre{0.000} \
\toprule
\end{tabular}
\end{center}
\setbeamercovered{} \begin{center} \begin{tikzpicture}[>=Stealth, overlay] % Rectangles \draw <2> [gray, very thick] (-1,0.3) rectangle (1,6.9); \draw <3> [gray, very thick] (1,0.3) rectangle (3.3,6.9); % 200 points ellipse \draw <4> [gray, very thick] (-3.5,0.3) rectangle (3.5,1.9); \end{tikzpicture} \end{center} \setbeamercovered{transparent}
Trapani samples results
\vspace{20pt}
\begin{center}
\begin{tabular}{rccccc}
\toprule
& & \multicolumn{2}{c}{L sample} & \multicolumn{2}{c}{M sample} \
& & \mu_1 & \mu_2 & \mu_1 & \mu_2 \
\midrule
\multirow{2}{}{50000} & \Theta & 0.255 & 0.432 & 106.1 & 162.5 \
& p & \gre{0.614} & \gre{0.511} & \gre{0.000} & \gre{0.000} \
\midrule
\multirow{2}{}{5000} & \Theta & 2.178 & 2.556 & 23.36 & 36.48 \
& p & \gre{0.140} & \gre{0.110} & \gre{0.000} & \gre{0.000} \
\midrule
\multirow{2}{*}{1000} & \Theta & 0.694 & 0.060 & 5.985 & 7.302 \
& p & \gre{0.405} & \gre{0.549} & \gre{0.014} & \gre{0.007} \
\toprule
\end{tabular}
\end{center}
\setbeamercovered{} \begin{center} \begin{tikzpicture}[>=Stealth, overlay] % Rectangles \draw <2,3> [gray, very thick] (-2,0.3) rectangle (1,6.1); \draw <4> [gray, very thick] (1,0.3) rectangle (4.2,6.1); % Estimations ellipses \draw <3> [cyclamen, thick] (-1.28,2.18) ellipse (0.7cm and 0.3cm); \draw <3> [cyclamen, thick] (0.29,2.18) ellipse (0.7cm and 0.3cm); \end{tikzpicture} \end{center} \setbeamercovered{transparent}