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Add normal distribution table
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Martin Thoma
parent
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7 changed files with 240 additions and 0 deletions
28
documents/normal-distribution/Makefile
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28
documents/normal-distribution/Makefile
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SOURCE=normal-distribution
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DELAY = 80
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DENSITY = 300
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WIDTH = 512
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make:
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pdflatex $(SOURCE).tex -output-format=pdf
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make clean
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clean:
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rm -rf $(TARGET) *.class *.html *.log *.aux *.out
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png:
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make
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make svg
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inkscape $(SOURCE).svg -w $(WIDTH) --export-png=$(SOURCE).png
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transparentGif:
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convert $(SOURCE).pdf -transparent white result.gif
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make clean
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svg:
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#inkscape $(SOURCE).pdf --export-plain-svg=$(SOURCE).svg
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pdf2svg $(SOURCE).pdf $(SOURCE).svg
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# Necessary, as pdf2svg does not always create valid svgs:
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inkscape $(SOURCE).svg --export-width=$(WIDTH) --export-plain-svg=$(SOURCE)1.svg
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rsvg-convert -a -w 720 -f svg $(SOURCE)1.svg -o $(SOURCE).svg
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rm $(SOURCE)1.svg
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8
documents/normal-distribution/README.md
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8
documents/normal-distribution/README.md
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Compiled example
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----------------
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## Credits
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Thanks to [Jake](http://tex.stackexchange.com/users/2552/jake) for the
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plot of the normal distribution ([link](http://tex.stackexchange.com/a/100030/5645))
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13
documents/normal-distribution/generate_numbers.py
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13
documents/normal-distribution/generate_numbers.py
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#!/usr/bin/env python
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"""Generate the LaTeX code for a table of the CDF of a normal distribution."""
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from scipy.stats import norm
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from numpy import arange
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for x in arange(0.0, 4.0, 0.1):
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line = "\\textbf{%0.1f} & " % x
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values = [norm.cdf(x+dx) for dx in arange(0.00, 0.09 + 0.01, 0.01)]
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values = ["%0.4f" % el for el in values]
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line += " & ".join(values)
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print(line + "\\\\")
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BIN
documents/normal-distribution/normal-distribution.pdf
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documents/normal-distribution/normal-distribution.pdf
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documents/normal-distribution/normal-distribution.png
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documents/normal-distribution/normal-distribution.png
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After Width: | Height: | Size: 134 KiB |
114
documents/normal-distribution/normal-distribution.tex
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documents/normal-distribution/normal-distribution.tex
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\documentclass[a4paper]{article}
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\usepackage[margin=20mm]{geometry}
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\usepackage[english]{babel}
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\usepackage[utf8]{inputenc}
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\usepackage{amssymb,amsmath}
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\usepackage{slashbox}
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\usepackage{booktabs}
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\usepackage[table,x11names]{xcolor}
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\usepackage{pgfplots}
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\setlength{\intextsep}{1pt}
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\begin{document}
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\section*{Normal distribution}
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\pgfmathdeclarefunction{gauss}{3}{%
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\pgfmathparse{1/(#3*sqrt(2*pi))*exp(-((#1-#2)^2)/(2*#3^2))}%
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}
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\begin{figure}[!h]
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\centering
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\begin{tikzpicture}
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\begin{axis}[
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no markers,
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domain=0:6,
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samples=100,
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ymin=0,
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axis lines*=left,
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xlabel=$x$,
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every axis y label/.style={at=(current axis.above origin),anchor=south},
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every axis x label/.style={at=(current axis.right of origin),anchor=west},
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height=4cm,
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width=12cm,
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xtick=\empty,
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ytick=\empty,
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enlargelimits=false,
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clip=false,
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axis on top,
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grid = major,
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hide y axis
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]
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\addplot [very thick,cyan!50!black] {gauss(x, 3, 1)};
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\pgfmathsetmacro\valueA{gauss(1,3,1)}
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\pgfmathsetmacro\valueB{gauss(2,3,1)}
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\draw [gray] (axis cs:1,0) -- (axis cs:1,\valueA)
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(axis cs:5,0) -- (axis cs:5,\valueA);
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\draw [gray] (axis cs:2,0) -- (axis cs:2,\valueB)
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(axis cs:4,0) -- (axis cs:4,\valueB);
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\draw [yshift=1.4cm, latex-latex](axis cs:2, 0) -- node [fill=white] {$0.683$} (axis cs:4, 0);
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\draw [yshift=0.3cm, latex-latex](axis cs:1, 0) -- node [fill=white] {$0.954$} (axis cs:5, 0);
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\node[below] at (axis cs:1, 0) {$\mu - 2\sigma$};
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\node[below] at (axis cs:2, 0) {$\mu - \sigma$};
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\node[below] at (axis cs:3, 0) {$\mu$};
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\end{axis}
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\end{tikzpicture}
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\end{figure}
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\begin{table}[!h]
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\centering
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\begin{tabular}{c|ccccc|ccccc}
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\toprule
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\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
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\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\\
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\textbf{0.1} & 0.5398 & 0.5438 & 0.5478 & 0.5517 & 0.5557 & 0.5596 & 0.5636 & 0.5675 & 0.5714 & 0.5753\\
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\textbf{0.2} & 0.5793 & 0.5832 & 0.5871 & 0.5910 & 0.5948 & 0.5987 & 0.6026 & 0.6064 & 0.6103 & 0.6141\\
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\textbf{0.3} & 0.6179 & 0.6217 & 0.6255 & 0.6293 & 0.6331 & 0.6368 & 0.6406 & 0.6443 & 0.6480 & 0.6517\\
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\textbf{0.4} & 0.6554 & 0.6591 & 0.6628 & 0.6664 & 0.6700 & 0.6736 & 0.6772 & 0.6808 & 0.6844 & 0.6879\\
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\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\\
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\textbf{0.6} & 0.7257 & 0.7291 & 0.7324 & 0.7357 & 0.7389 & 0.7422 & 0.7454 & 0.7486 & 0.7517 & 0.7549\\
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\textbf{0.7} & 0.7580 & 0.7611 & 0.7642 & 0.7673 & 0.7704 & 0.7734 & 0.7764 & 0.7794 & 0.7823 & 0.7852\\
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\textbf{0.8} & 0.7881 & 0.7910 & 0.7939 & 0.7967 & 0.7995 & 0.8023 & 0.8051 & 0.8078 & 0.8106 & 0.8133\\
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\textbf{0.9} & 0.8159 & 0.8186 & 0.8212 & 0.8238 & 0.8264 & 0.8289 & 0.8315 & 0.8340 & 0.8365 & 0.8389\\
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\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\\
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\textbf{1.1} & 0.8643 & 0.8665 & 0.8686 & 0.8708 & 0.8729 & 0.8749 & 0.8770 & 0.8790 & 0.8810 & 0.8830\\
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\textbf{1.2} & 0.8849 & 0.8869 & 0.8888 & 0.8907 & 0.8925 & 0.8944 & 0.8962 & 0.8980 & 0.8997 & 0.9015\\
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\textbf{1.3} & 0.9032 & 0.9049 & 0.9066 & 0.9082 & 0.9099 & 0.9115 & 0.9131 & 0.9147 & 0.9162 & 0.9177\\
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\textbf{1.4} & 0.9192 & 0.9207 & 0.9222 & 0.9236 & 0.9251 & 0.9265 & 0.9279 & 0.9292 & 0.9306 & 0.9319\\
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\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\\
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\textbf{1.6} & 0.9452 & 0.9463 & 0.9474 & 0.9484 & 0.9495 & 0.9505 & 0.9515 & 0.9525 & 0.9535 & 0.9545\\
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\textbf{1.7} & 0.9554 & 0.9564 & 0.9573 & 0.9582 & 0.9591 & 0.9599 & 0.9608 & 0.9616 & 0.9625 & 0.9633\\
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\textbf{1.8} & 0.9641 & 0.9649 & 0.9656 & 0.9664 & 0.9671 & 0.9678 & 0.9686 & 0.9693 & 0.9699 & 0.9706\\
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\textbf{1.9} & 0.9713 & 0.9719 & 0.9726 & 0.9732 & 0.9738 & 0.9744 & 0.9750 & 0.9756 & 0.9761 & 0.9767\\
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\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\\
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\textbf{2.1} & 0.9821 & 0.9826 & 0.9830 & 0.9834 & 0.9838 & 0.9842 & 0.9846 & 0.9850 & 0.9854 & 0.9857\\
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\textbf{2.2} & 0.9861 & 0.9864 & 0.9868 & 0.9871 & 0.9875 & 0.9878 & 0.9881 & 0.9884 & 0.9887 & 0.9890\\
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\textbf{2.3} & 0.9893 & 0.9896 & 0.9898 & 0.9901 & 0.9904 & 0.9906 & 0.9909 & 0.9911 & 0.9913 & 0.9916\\
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\textbf{2.4} & 0.9918 & 0.9920 & 0.9922 & 0.9925 & 0.9927 & 0.9929 & 0.9931 & 0.9932 & 0.9934 & 0.9936\\
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\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\\
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\textbf{2.6} & 0.9953 & 0.9955 & 0.9956 & 0.9957 & 0.9959 & 0.9960 & 0.9961 & 0.9962 & 0.9963 & 0.9964\\
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\textbf{2.7} & 0.9965 & 0.9966 & 0.9967 & 0.9968 & 0.9969 & 0.9970 & 0.9971 & 0.9972 & 0.9973 & 0.9974\\
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\textbf{2.8} & 0.9974 & 0.9975 & 0.9976 & 0.9977 & 0.9977 & 0.9978 & 0.9979 & 0.9979 & 0.9980 & 0.9981\\
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\textbf{2.9} & 0.9981 & 0.9982 & 0.9982 & 0.9983 & 0.9984 & 0.9984 & 0.9985 & 0.9985 & 0.9986 & 0.9986\\
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\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\\
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\textbf{3.1} & 0.9990 & 0.9991 & 0.9991 & 0.9991 & 0.9992 & 0.9992 & 0.9992 & 0.9992 & 0.9993 & 0.9993\\
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\textbf{3.2} & 0.9993 & 0.9993 & 0.9994 & 0.9994 & 0.9994 & 0.9994 & 0.9994 & 0.9995 & 0.9995 & 0.9995\\
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\textbf{3.3} & 0.9995 & 0.9995 & 0.9995 & 0.9996 & 0.9996 & 0.9996 & 0.9996 & 0.9996 & 0.9996 & 0.9997\\
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\textbf{3.4} & 0.9997 & 0.9997 & 0.9997 & 0.9997 & 0.9997 & 0.9997 & 0.9997 & 0.9997 & 0.9997 & 0.9998\\
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\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\\
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\textbf{3.6} & 0.9998 & 0.9998 & 0.9999 & 0.9999 & 0.9999 & 0.9999 & 0.9999 & 0.9999 & 0.9999 & 0.9999\\
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\textbf{3.7} & 0.9999 & 0.9999 & 0.9999 & 0.9999 & 0.9999 & 0.9999 & 0.9999 & 0.9999 & 0.9999 & 0.9999\\
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\textbf{3.8} & 0.9999 & 0.9999 & 0.9999 & 0.9999 & 0.9999 & 0.9999 & 0.9999 & 0.9999 & 0.9999 & 0.9999\\
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\textbf{3.9} & 1.0000 & 1.0000 & 1.0000 & 1.0000 & 1.0000 & 1.0000 & 1.0000 & 1.0000 & 1.0000 & 1.0000\\
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\bottomrule
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\end{tabular}
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\caption{$\Phi_{0;1}(x + \Delta x)$}
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\end{table}
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\begin{align*}
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\Phi_{\mu; \sigma^2}(x) &= \Phi_{0;1} \left (\frac{x-\mu}{\sigma} \right ) &
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\Phi_{0;1}(-x) &= 1 - \Phi_{0;1}(x)
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\end{align*}
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\end{document}
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77
documents/normal-distribution/slashbox.sty
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documents/normal-distribution/slashbox.sty
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% slashbox.sty by Koichi Yasuoka, May 27, 1993
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% minor modification by Toru Sato, May 31, 1993
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\typeout{slashbox style by K.Yasuoka, May 1993.}%
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\newbox\@slashboxa
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\newbox\@slashboxb
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\newbox\@slashboxc
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\newcount\@slashboxwd
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\newcount\@slashboxht
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\newdimen\@slashsepl
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\newdimen\@slashsepr
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\def\slashbox{%
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\def\@slashboxpicture##1{%
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\put(0,0){\line(##1,1){\@slashboxwd}}%
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\put(0,\@slashboxht){\makebox(0,0)[tl]{\box\@slashboxa}}%
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\put(\@slashboxwd,0){\makebox(0,0)[br]{\box\@slashboxb}}%
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}%
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\@slashbox
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}%
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\def\backslashbox{%
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\def\@slashboxpicture##1{%
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\put(0,\@slashboxht){\line(##1,-1){\@slashboxwd}}%
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\put(0,0){\makebox(0,0)[bl]{\box\@slashboxa}}%
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\put(\@slashboxwd,\@slashboxht){\makebox(0,0)[tr]{\box\@slashboxb}}%
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}%
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\@slashbox
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}%
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\def\@slashbox{\@ifnextchar [{\@@slashbox}{\@@slashbox[0pt]}}
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\def\@@slashbox[#1]{\@ifnextchar [{\@@@slashbox[#1]}{\@@@slashbox[#1][c]}}
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\def\@@@slashbox[#1][#2]#3#4{%
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% #1: width, #2: suppression of \tabcolsep on `l', `r', or `lr' side
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% #3: left item, #4: right item
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\@slashsepl=\tabcolsep
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\@slashsepr=\tabcolsep
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\@tfor\@tempa :=#2\do{\expandafter\let
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\csname @slashsep\@tempa\endcsname=\z@}%
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\setbox\@slashboxa=\hbox{\strut\hskip\tabcolsep\shortstack[l]{#3}}%
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\setbox\@slashboxb=\hbox{\shortstack[r]{#4}\hskip\tabcolsep\strut}%
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\setbox\@slashboxa=\hbox{\raise\dp\@slashboxa\box\@slashboxa}%
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\setbox\@slashboxb=\hbox{\raise\dp\@slashboxb\box\@slashboxb}%
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\setbox\@slashboxc=\hbox{%
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\@tempdima=\wd\@slashboxa
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\advance\@tempdima by \wd\@slashboxb
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\advance\@tempdima by \@slashsepl
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\advance\@tempdima by \@slashsepr
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\@tempdimb=#1\relax%
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\ifdim\@tempdimb>\@tempdima \@tempdima=\@tempdimb\fi%
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\@tempdimb=\ht\@slashboxa
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\advance\@tempdimb by \dp\@slashboxa
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\advance\@tempdimb by \ht\@slashboxb
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\advance\@tempdimb by \dp\@slashboxb
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\@tempcnta=\@tempdima
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\@tempcntb=\@tempdimb
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\advance\@tempcnta by \@tempcntb
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\advance\@tempcnta by -1
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\divide\@tempcnta by \@tempcntb
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\ifnum\@tempcnta>6 \@tempcnta=6
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\@tempdimb=0.166666666\@tempdima
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\else
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\ifnum\@tempcnta<1 \@tempcnta=1\fi
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\@tempdima=\@tempdimb
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\multiply\@tempdima by \@tempcnta
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\fi%
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\advance\@tempdima by -\@slashsepl
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\advance\@tempdima by -\@slashsepr
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\@slashboxwd=\@tempdima
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\@slashboxht=\@tempdimb
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\@tempcntb=\@slashsepl
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\setlength{\unitlength}{1sp}%
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\begin{picture}(\@slashboxwd,\@slashboxht)(\@tempcntb,0)
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\advance\@tempdima by \@slashsepl
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\advance\@tempdima by \@slashsepr
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\@slashboxwd=\@tempdima
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\@slashboxpicture{\@tempcnta}
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\end{picture}%
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}%
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$\vcenter{\box\@slashboxc}$%
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}%
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