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more guide plots

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Dima Kogan
2021-02-20 20:08:13 -08:00
parent f3542ba620
commit 2463336cbf
3 changed files with 2018 additions and 125 deletions
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guide/guide.org
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@@ -435,19 +435,48 @@ samples in [-1,1]: it should be normal-ish. And let's draw the expected perfect
PDF on top (as an equation, evaluated by =gnuplot=).
#+BEGIN_SRC sh :results file link :exports both
N=1000;
Nsum=200;
var=$((Nsum/3));
binwidth=2;
N=20000;
Nsum=10;
binwidth=.1;
seq $N | \
perl -nE '$Nsum = '$Nsum';
$var = '$Nsum' / 3.;
$s = 0; for $i (1..$Nsum) { $s += rand()*2-1; }
say $s;' | \
say $s/sqrt($var);' | \
feedgnuplot --histo 0 --binwidth $binwidth \
--equation-above "($N * sqrt(2.*pi*$var) * erf($binwidth/(2.*sqrt(2.*$var)))) * \
exp(-(x*x)/(2.*$var)) / \
sqrt(2.*pi*$var) title \"Limit gaussian\" with lines lw 2"
--equation-above "($N * sqrt(2.*pi) * erf($binwidth/(2.*sqrt(2.)))) * \
exp(-(x*x)/(2.)) / \
sqrt(2.*pi) title \"Limit gaussian\" with lines lw 2"
#+END_SRC
#+RESULTS:
[[file:guide-16.svg]]
If we want multiple histograms drawn on top of one another, the styling should
be adjusted so that they both remain visible. Let's vary the size of the sum,
and look at the effects: bigger sums should be more gaussian-like:
#+BEGIN_SRC sh :results file link :exports both
N=20000;
binwidth=.1;
for Nsum in 1 2 3; do
seq $N | \
perl -nE '$, = " ";
$Nsum = '$Nsum';
$var = '$Nsum' / 3.;
$s = 0; for $i (1..$Nsum) { $s += rand()*2-1; }
say $Nsum,$s/sqrt($var);';
done | \
feedgnuplot --dataid --histo 1,2,3 --binwidth $binwidth \
--autolegend \
--style 1 'with boxes fill transparent solid 0.3 border lt -1' \
--style 2 'with boxes fill transparent pattern 4 border lt -1' \
--style 3 'with boxes fill transparent pattern 5 border lt -1' \
--equation-above "($N * sqrt(2.*pi) * erf($binwidth/(2.*sqrt(2.)))) * \
exp(-(x*x)/(2.)) / \
sqrt(2.*pi) title \"Limit gaussian\" with lines lw 2"
#+END_SRC
#+RESULTS:
[[file:guide-17.svg]]