From 4983c8c734701013312b3551675bf7ca38def02c Mon Sep 17 00:00:00 2001 From: Martin Thoma Date: Sun, 27 Mar 2016 14:24:27 +0200 Subject: [PATCH] Add normal distribution table --- documents/normal-distribution/Makefile | 28 +++++ documents/normal-distribution/README.md | 8 ++ .../normal-distribution/generate_numbers.py | 13 ++ .../normal-distribution.pdf | Bin 0 -> 85536 bytes .../normal-distribution.png | Bin 0 -> 137581 bytes .../normal-distribution.tex | 114 ++++++++++++++++++ documents/normal-distribution/slashbox.sty | 77 ++++++++++++ 7 files changed, 240 insertions(+) create mode 100644 documents/normal-distribution/Makefile create mode 100644 documents/normal-distribution/README.md create mode 100644 documents/normal-distribution/generate_numbers.py create mode 100644 documents/normal-distribution/normal-distribution.pdf create mode 100644 documents/normal-distribution/normal-distribution.png create mode 100644 documents/normal-distribution/normal-distribution.tex create mode 100644 documents/normal-distribution/slashbox.sty diff --git a/documents/normal-distribution/Makefile b/documents/normal-distribution/Makefile new file mode 100644 index 0000000..e5ff2cb --- /dev/null +++ b/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 $(SOURCE)1.svg diff --git a/documents/normal-distribution/README.md b/documents/normal-distribution/README.md new file mode 100644 index 0000000..6b64626 --- /dev/null +++ b/documents/normal-distribution/README.md @@ -0,0 +1,8 @@ +Compiled example +---------------- +![Example](normal-distribution.png) + +## Credits + +Thanks to [Jake](http://tex.stackexchange.com/users/2552/jake) for the +plot of the normal distribution ([link](http://tex.stackexchange.com/a/100030/5645)) \ No newline at end of file diff --git a/documents/normal-distribution/generate_numbers.py b/documents/normal-distribution/generate_numbers.py new file mode 100644 index 0000000..51e17e0 --- /dev/null +++ b/documents/normal-distribution/generate_numbers.py @@ -0,0 +1,13 @@ +#!/usr/bin/env python + +"""Generate the LaTeX code for a table of the CDF of a normal distribution.""" + +from scipy.stats import norm +from numpy import arange + +for x in arange(0.0, 4.0, 0.1): + line = "\\textbf{%0.1f} & " % x + values = [norm.cdf(x+dx) for dx in arange(0.00, 0.09 + 0.01, 0.01)] + values = ["%0.4f" % el for el in values] + line += " & ".join(values) + print(line + "\\\\") diff --git a/documents/normal-distribution/normal-distribution.pdf b/documents/normal-distribution/normal-distribution.pdf new file mode 100644 index 0000000000000000000000000000000000000000..cfcf2a4963e9165cab3aa9d5382317222f535d9a GIT binary patch literal 85536 zcma&NV{k7~^EDdVwr$&XPOKB#wv!Xvww;{Vwr$&X^2TOocfC=-80`W(DP5zX|28T7H`X{+P#*h&JT-< zs2Yd8iU&Uu1#!oDUx4YfjkCpl&dyy%maV1-Zh6kbl<@>{kFwK`!FTt~*^WfaK>3#) zCwxC`p8Z)t#lKJb_N>})6bgN$DM{>bsWE{a{^>hi6U6bR^UBe&Rf!V}o8dGQXze3d zDfFI89#z4NY6!j_ShMBDzS&vgDNd1wB&Oj$=Xp&s_znV!GBxGej@Q~4{=?&xEo0lU9i6dpH%JGOTnNAjo=CJ+> z4soaA%AlRjR+$$rE-&P;voQ3&#oE!f{n-lo3@1E)~g(cs`2) zkX*$_0f@9+N}HnRq)p&a3Y1StyrU-|MeD;sy%dg5p=)Zi2qc{?T5uL#OrCa_LXHO%0+A=1|mD3Mv~RgGK(PWjg1=+CjKD8U^> zlMa>WVvFFPkf1{8eP=LOH>k@RpOav#Lp<*!B&Q&#Y@N>7H?%xQ3}VFyDdKW}ou9~f zBq`oetkIs7XrOuoj5|)vk8BPPGTRtkeiSnui8Gunh&=Ft%M}}#g)#kkON7s$?tAYJ 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+\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} diff --git a/documents/normal-distribution/slashbox.sty b/documents/normal-distribution/slashbox.sty new file mode 100644 index 0000000..1712c9e --- /dev/null +++ b/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}}% + 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