Add normal distribution table

documents/normal-distribution/Makefile

@@ -0,0 +1,28 @@
+SOURCE=normal-distribution
+DELAY = 80
+DENSITY = 300
+WIDTH = 512
+
+make:
+	pdflatex $(SOURCE).tex -output-format=pdf
+	make clean
+
+clean:
+	rm -rf  $(TARGET) *.class *.html *.log *.aux *.out
+
+png:
+	make
+	make svg
+	inkscape $(SOURCE).svg -w $(WIDTH) --export-png=$(SOURCE).png
+
+transparentGif:
+	convert $(SOURCE).pdf -transparent white result.gif
+	make clean
+
+svg:
+	#inkscape $(SOURCE).pdf --export-plain-svg=$(SOURCE).svg
+	pdf2svg $(SOURCE).pdf $(SOURCE).svg
+	# Necessary, as pdf2svg does not always create valid svgs:
+	inkscape $(SOURCE).svg --export-width=$(WIDTH) --export-plain-svg=$(SOURCE)1.svg
+	rsvg-convert -a -w 720 -f svg $(SOURCE)1.svg -o $(SOURCE).svg
+	rm $(SOURCE)1.svg

documents/normal-distribution/README.md

@@ -0,0 +1,8 @@
+Compiled example
+----------------
+![Example](normal-distribution.png)
+
+## Credits
+
+Thanks to [Jake](http://tex.stackexchange.com/users/2552/jake) for the
+plot of the normal distribution ([link](http://tex.stackexchange.com/a/100030/5645))

documents/normal-distribution/generate_numbers.py

@@ -0,0 +1,13 @@
+#!/usr/bin/env python
+
+"""Generate the LaTeX code for a table of the CDF of a normal distribution."""
+
+from scipy.stats import norm
+from numpy import arange
+
+for x in arange(0.0, 4.0, 0.1):
+    line = "\\textbf{%0.1f} & " % x
+    values = [norm.cdf(x+dx) for dx in arange(0.00, 0.09 + 0.01, 0.01)]
+    values = ["%0.4f" % el for el in values]
+    line += " & ".join(values)
+    print(line + "\\\\")

documents/normal-distribution/normal-distribution.tex

@@ -0,0 +1,114 @@
+\documentclass[a4paper]{article}
+\usepackage[margin=20mm]{geometry}
+\usepackage[english]{babel}
+\usepackage[utf8]{inputenc}
+\usepackage{amssymb,amsmath}
+\usepackage{slashbox}
+\usepackage{booktabs}
+\usepackage[table,x11names]{xcolor}
+\usepackage{pgfplots}
+
+\setlength{\intextsep}{1pt}
+
+\begin{document}
+    \section*{Normal distribution}
+
+\pgfmathdeclarefunction{gauss}{3}{%
+  \pgfmathparse{1/(#3*sqrt(2*pi))*exp(-((#1-#2)^2)/(2*#3^2))}%
+}
+
+\begin{figure}[!h]
+\centering
+\begin{tikzpicture}
+\begin{axis}[
+  no markers,
+  domain=0:6,
+  samples=100,
+  ymin=0,
+  axis lines*=left,
+  xlabel=$x$,
+  every axis y label/.style={at=(current axis.above origin),anchor=south},
+  every axis x label/.style={at=(current axis.right of origin),anchor=west},
+  height=4cm,
+  width=12cm,
+  xtick=\empty,
+  ytick=\empty,
+  enlargelimits=false,
+  clip=false,
+  axis on top,
+  grid = major,
+  hide y axis
+  ]
+
+ \addplot [very thick,cyan!50!black] {gauss(x, 3, 1)};
+
+\pgfmathsetmacro\valueA{gauss(1,3,1)}
+\pgfmathsetmacro\valueB{gauss(2,3,1)}
+\draw [gray] (axis cs:1,0) -- (axis cs:1,\valueA)
+    (axis cs:5,0) -- (axis cs:5,\valueA);
+\draw [gray] (axis cs:2,0) -- (axis cs:2,\valueB)
+    (axis cs:4,0) -- (axis cs:4,\valueB);
+\draw [yshift=1.4cm, latex-latex](axis cs:2, 0) -- node [fill=white] {$0.683$} (axis cs:4, 0);
+\draw [yshift=0.3cm, latex-latex](axis cs:1, 0) -- node [fill=white] {$0.954$} (axis cs:5, 0);
+
+\node[below] at (axis cs:1, 0)  {$\mu - 2\sigma$};
+\node[below] at (axis cs:2, 0)  {$\mu - \sigma$};
+\node[below] at (axis cs:3, 0)  {$\mu$};
+\end{axis}
+\end{tikzpicture}
+\end{figure}
+
+\begin{table}[!h]
+    \centering
+    \begin{tabular}{c|ccccc|ccccc}
+    \toprule
+    \backslashbox{$x$}{$\Delta x$}  & \textbf{0.00} & \textbf{0.01} & \textbf{0.02} & \textbf{0.03} & \textbf{0.04} & \textbf{0.05} & \textbf{0.06} & \textbf{0.07} & \textbf{0.08} & \textbf{0.09} \\\midrule
+\rowcolor{lightgray}\textbf{0.0} & 0.5000 & 0.5040 & 0.5080 & 0.5120 & 0.5160 & 0.5199 & 0.5239 & 0.5279 & 0.5319 & 0.5359\\
+\textbf{0.1} & 0.5398 & 0.5438 & 0.5478 & 0.5517 & 0.5557 & 0.5596 & 0.5636 & 0.5675 & 0.5714 & 0.5753\\
+\textbf{0.2} & 0.5793 & 0.5832 & 0.5871 & 0.5910 & 0.5948 & 0.5987 & 0.6026 & 0.6064 & 0.6103 & 0.6141\\
+\textbf{0.3} & 0.6179 & 0.6217 & 0.6255 & 0.6293 & 0.6331 & 0.6368 & 0.6406 & 0.6443 & 0.6480 & 0.6517\\
+\textbf{0.4} & 0.6554 & 0.6591 & 0.6628 & 0.6664 & 0.6700 & 0.6736 & 0.6772 & 0.6808 & 0.6844 & 0.6879\\
+\rowcolor{lightgray}\textbf{0.5} & 0.6915 & 0.6950 & 0.6985 & 0.7019 & 0.7054 & 0.7088 & 0.7123 & 0.7157 & 0.7190 & 0.7224\\
+\textbf{0.6} & 0.7257 & 0.7291 & 0.7324 & 0.7357 & 0.7389 & 0.7422 & 0.7454 & 0.7486 & 0.7517 & 0.7549\\
+\textbf{0.7} & 0.7580 & 0.7611 & 0.7642 & 0.7673 & 0.7704 & 0.7734 & 0.7764 & 0.7794 & 0.7823 & 0.7852\\
+\textbf{0.8} & 0.7881 & 0.7910 & 0.7939 & 0.7967 & 0.7995 & 0.8023 & 0.8051 & 0.8078 & 0.8106 & 0.8133\\
+\textbf{0.9} & 0.8159 & 0.8186 & 0.8212 & 0.8238 & 0.8264 & 0.8289 & 0.8315 & 0.8340 & 0.8365 & 0.8389\\
+\rowcolor{lightgray}\textbf{1.0} & 0.8413 & 0.8438 & 0.8461 & 0.8485 & 0.8508 & 0.8531 & 0.8554 & 0.8577 & 0.8599 & 0.8621\\
+\textbf{1.1} & 0.8643 & 0.8665 & 0.8686 & 0.8708 & 0.8729 & 0.8749 & 0.8770 & 0.8790 & 0.8810 & 0.8830\\
+\textbf{1.2} & 0.8849 & 0.8869 & 0.8888 & 0.8907 & 0.8925 & 0.8944 & 0.8962 & 0.8980 & 0.8997 & 0.9015\\
+\textbf{1.3} & 0.9032 & 0.9049 & 0.9066 & 0.9082 & 0.9099 & 0.9115 & 0.9131 & 0.9147 & 0.9162 & 0.9177\\
+\textbf{1.4} & 0.9192 & 0.9207 & 0.9222 & 0.9236 & 0.9251 & 0.9265 & 0.9279 & 0.9292 & 0.9306 & 0.9319\\
+\rowcolor{lightgray}\textbf{1.5} & 0.9332 & 0.9345 & 0.9357 & 0.9370 & 0.9382 & 0.9394 & 0.9406 & 0.9418 & 0.9429 & 0.9441\\
+\textbf{1.6} & 0.9452 & 0.9463 & 0.9474 & 0.9484 & 0.9495 & 0.9505 & 0.9515 & 0.9525 & 0.9535 & 0.9545\\
+\textbf{1.7} & 0.9554 & 0.9564 & 0.9573 & 0.9582 & 0.9591 & 0.9599 & 0.9608 & 0.9616 & 0.9625 & 0.9633\\
+\textbf{1.8} & 0.9641 & 0.9649 & 0.9656 & 0.9664 & 0.9671 & 0.9678 & 0.9686 & 0.9693 & 0.9699 & 0.9706\\
+\textbf{1.9} & 0.9713 & 0.9719 & 0.9726 & 0.9732 & 0.9738 & 0.9744 & 0.9750 & 0.9756 & 0.9761 & 0.9767\\
+\rowcolor{lightgray}\textbf{2.0} & 0.9772 & 0.9778 & 0.9783 & 0.9788 & 0.9793 & 0.9798 & 0.9803 & 0.9808 & 0.9812 & 0.9817\\
+\textbf{2.1} & 0.9821 & 0.9826 & 0.9830 & 0.9834 & 0.9838 & 0.9842 & 0.9846 & 0.9850 & 0.9854 & 0.9857\\
+\textbf{2.2} & 0.9861 & 0.9864 & 0.9868 & 0.9871 & 0.9875 & 0.9878 & 0.9881 & 0.9884 & 0.9887 & 0.9890\\
+\textbf{2.3} & 0.9893 & 0.9896 & 0.9898 & 0.9901 & 0.9904 & 0.9906 & 0.9909 & 0.9911 & 0.9913 & 0.9916\\
+\textbf{2.4} & 0.9918 & 0.9920 & 0.9922 & 0.9925 & 0.9927 & 0.9929 & 0.9931 & 0.9932 & 0.9934 & 0.9936\\
+\rowcolor{lightgray}\textbf{2.5} & 0.9938 & 0.9940 & 0.9941 & 0.9943 & 0.9945 & 0.9946 & 0.9948 & 0.9949 & 0.9951 & 0.9952\\
+\textbf{2.6} & 0.9953 & 0.9955 & 0.9956 & 0.9957 & 0.9959 & 0.9960 & 0.9961 & 0.9962 & 0.9963 & 0.9964\\
+\textbf{2.7} & 0.9965 & 0.9966 & 0.9967 & 0.9968 & 0.9969 & 0.9970 & 0.9971 & 0.9972 & 0.9973 & 0.9974\\
+\textbf{2.8} & 0.9974 & 0.9975 & 0.9976 & 0.9977 & 0.9977 & 0.9978 & 0.9979 & 0.9979 & 0.9980 & 0.9981\\
+\textbf{2.9} & 0.9981 & 0.9982 & 0.9982 & 0.9983 & 0.9984 & 0.9984 & 0.9985 & 0.9985 & 0.9986 & 0.9986\\
+\rowcolor{lightgray}\textbf{3.0} & 0.9987 & 0.9987 & 0.9987 & 0.9988 & 0.9988 & 0.9989 & 0.9989 & 0.9989 & 0.9990 & 0.9990\\
+\textbf{3.1} & 0.9990 & 0.9991 & 0.9991 & 0.9991 & 0.9992 & 0.9992 & 0.9992 & 0.9992 & 0.9993 & 0.9993\\
+\textbf{3.2} & 0.9993 & 0.9993 & 0.9994 & 0.9994 & 0.9994 & 0.9994 & 0.9994 & 0.9995 & 0.9995 & 0.9995\\
+\textbf{3.3} & 0.9995 & 0.9995 & 0.9995 & 0.9996 & 0.9996 & 0.9996 & 0.9996 & 0.9996 & 0.9996 & 0.9997\\
+\textbf{3.4} & 0.9997 & 0.9997 & 0.9997 & 0.9997 & 0.9997 & 0.9997 & 0.9997 & 0.9997 & 0.9997 & 0.9998\\
+\rowcolor{lightgray}\textbf{3.5} & 0.9998 & 0.9998 & 0.9998 & 0.9998 & 0.9998 & 0.9998 & 0.9998 & 0.9998 & 0.9998 & 0.9998\\
+\textbf{3.6} & 0.9998 & 0.9998 & 0.9999 & 0.9999 & 0.9999 & 0.9999 & 0.9999 & 0.9999 & 0.9999 & 0.9999\\
+\textbf{3.7} & 0.9999 & 0.9999 & 0.9999 & 0.9999 & 0.9999 & 0.9999 & 0.9999 & 0.9999 & 0.9999 & 0.9999\\
+\textbf{3.8} & 0.9999 & 0.9999 & 0.9999 & 0.9999 & 0.9999 & 0.9999 & 0.9999 & 0.9999 & 0.9999 & 0.9999\\
+\textbf{3.9} & 1.0000 & 1.0000 & 1.0000 & 1.0000 & 1.0000 & 1.0000 & 1.0000 & 1.0000 & 1.0000 & 1.0000\\
+        \bottomrule
+        \end{tabular}
+        \caption{$\Phi_{0;1}(x + \Delta x)$}
+    \end{table}
+    \begin{align*}
+        \Phi_{\mu; \sigma^2}(x) &= \Phi_{0;1} \left (\frac{x-\mu}{\sigma} \right ) &
+        \Phi_{0;1}(-x) &= 1 - \Phi_{0;1}(x)
+    \end{align*}
+\end{document}

documents/normal-distribution/slashbox.sty

@@ -0,0 +1,77 @@
+% slashbox.sty by Koichi Yasuoka, May 27, 1993
+%              minor modification by Toru Sato, May 31, 1993
+\typeout{slashbox style by K.Yasuoka, May 1993.}%
+\newbox\@slashboxa
+\newbox\@slashboxb
+\newbox\@slashboxc
+\newcount\@slashboxwd
+\newcount\@slashboxht
+\newdimen\@slashsepl
+\newdimen\@slashsepr
+\def\slashbox{%
+  \def\@slashboxpicture##1{%
+    \put(0,0){\line(##1,1){\@slashboxwd}}%
+    \put(0,\@slashboxht){\makebox(0,0)[tl]{\box\@slashboxa}}%
+    \put(\@slashboxwd,0){\makebox(0,0)[br]{\box\@slashboxb}}%
+  }%
+  \@slashbox
+}%
+\def\backslashbox{%
+  \def\@slashboxpicture##1{%
+    \put(0,\@slashboxht){\line(##1,-1){\@slashboxwd}}%
+    \put(0,0){\makebox(0,0)[bl]{\box\@slashboxa}}%
+    \put(\@slashboxwd,\@slashboxht){\makebox(0,0)[tr]{\box\@slashboxb}}%
+  }%
+  \@slashbox
+}%
+\def\@slashbox{\@ifnextchar [{\@@slashbox}{\@@slashbox[0pt]}}
+\def\@@slashbox[#1]{\@ifnextchar [{\@@@slashbox[#1]}{\@@@slashbox[#1][c]}}
+\def\@@@slashbox[#1][#2]#3#4{%
+% #1: width, #2: suppression of \tabcolsep on `l', `r', or `lr' side
+% #3: left item, #4: right item
+  \@slashsepl=\tabcolsep
+  \@slashsepr=\tabcolsep
+    \@tfor\@tempa :=#2\do{\expandafter\let
+        \csname @slashsep\@tempa\endcsname=\z@}%
+  \setbox\@slashboxa=\hbox{\strut\hskip\tabcolsep\shortstack[l]{#3}}%
+  \setbox\@slashboxb=\hbox{\shortstack[r]{#4}\hskip\tabcolsep\strut}%
+  \setbox\@slashboxa=\hbox{\raise\dp\@slashboxa\box\@slashboxa}%
+  \setbox\@slashboxb=\hbox{\raise\dp\@slashboxb\box\@slashboxb}%
+  \setbox\@slashboxc=\hbox{%
+    \@tempdima=\wd\@slashboxa
+    \advance\@tempdima by \wd\@slashboxb
+    \advance\@tempdima by \@slashsepl
+    \advance\@tempdima by \@slashsepr
+    \@tempdimb=#1\relax%
+    \ifdim\@tempdimb>\@tempdima \@tempdima=\@tempdimb\fi%
+    \@tempdimb=\ht\@slashboxa
+    \advance\@tempdimb by \dp\@slashboxa
+    \advance\@tempdimb by \ht\@slashboxb
+    \advance\@tempdimb by \dp\@slashboxb
+    \@tempcnta=\@tempdima
+    \@tempcntb=\@tempdimb
+    \advance\@tempcnta by \@tempcntb
+    \advance\@tempcnta by -1
+    \divide\@tempcnta by \@tempcntb
+    \ifnum\@tempcnta>6 \@tempcnta=6
+      \@tempdimb=0.166666666\@tempdima
+    \else
+      \ifnum\@tempcnta<1 \@tempcnta=1\fi
+      \@tempdima=\@tempdimb
+      \multiply\@tempdima by \@tempcnta
+    \fi%
+    \advance\@tempdima by -\@slashsepl
+    \advance\@tempdima by -\@slashsepr
+    \@slashboxwd=\@tempdima
+    \@slashboxht=\@tempdimb
+    \@tempcntb=\@slashsepl
+    \setlength{\unitlength}{1sp}%
+    \begin{picture}(\@slashboxwd,\@slashboxht)(\@tempcntb,0)
+    \advance\@tempdima by \@slashsepl
+    \advance\@tempdima by \@slashsepr
+    \@slashboxwd=\@tempdima
+    \@slashboxpicture{\@tempcnta}
+    \end{picture}%
+  }%
+  $\vcenter{\box\@slashboxc}$%
+}%