Randomizing examples¶
Generating random numbers from various distributions¶
Here we can chain together a few simple building blocks:
cat expo-sample.sh
# Generate 100,000 pairs of independent and identically distributed
# exponentially distributed random variables with the same rate parameter
# (namely, 2.5). Then compute histograms of one of them, along with
# histograms for their sum and their product.
#
# See also https://en.wikipedia.org/wiki/Exponential_distribution
#
# Here I'm using a specified random-number seed so this example always
# produces the same output for this web document: in everyday practice we
# wouldn't do that.
mlr -n \
--seed 0 \
--opprint \
seqgen --stop 100000 \
then put '
# https://en.wikipedia.org/wiki/Inverse_transform_sampling
func expo_sample(lambda) {
return -log(1-urand())/lambda
}
$u = expo_sample(2.5);
$v = expo_sample(2.5);
$s = $u + $v;
$p = $u * $v;
' \
then histogram -f u,s,p --lo 0 --hi 2 --nbins 50 \
then bar -f u_count,s_count,p_count --auto -w 20
Namely:
Set the Miller random-number seed so this webdoc looks the same every time I regenerate it.
Use pretty-printed tabular output.
Use pretty-printed tabular output.
Use
seqgento produce 100,000 recordsi=0,i=1, etc.Send those to a
putstep which defines an inverse-transform-sampling function and calls it twice, then computes the sum and product of samples.Send those to a histogram, and from there to a bar-plotter. This is just for visualization; you could just as well output CSV and send that off to your own plotting tool, etc.
The output is as follows:
sh expo-sample.sh
bin_lo bin_hi u_count s_count p_count
0 0.04 [64]*******************#[9554] [326]#...................[3703] [19]*******************#[39809]
0.04 0.08 [64]*****************...[9554] [326]*****...............[3703] [19]*******.............[39809]
0.08 0.12 [64]****************....[9554] [326]*********...........[3703] [19]****................[39809]
0.12 0.16 [64]**************......[9554] [326]************........[3703] [19]***.................[39809]
0.16 0.2 [64]*************.......[9554] [326]**************......[3703] [19]**..................[39809]
0.2 0.24 [64]************........[9554] [326]*****************...[3703] [19]*...................[39809]
0.24 0.28 [64]**********..........[9554] [326]******************..[3703] [19]*...................[39809]
0.28 0.32 [64]*********...........[9554] [326]******************..[3703] [19]*...................[39809]
0.32 0.36 [64]********............[9554] [326]*******************.[3703] [19]#...................[39809]
0.36 0.4 [64]*******.............[9554] [326]*******************#[3703] [19]#...................[39809]
0.4 0.44 [64]*******.............[9554] [326]*******************.[3703] [19]#...................[39809]
0.44 0.48 [64]******..............[9554] [326]*******************.[3703] [19]#...................[39809]
0.48 0.52 [64]*****...............[9554] [326]******************..[3703] [19]#...................[39809]
0.52 0.56 [64]*****...............[9554] [326]******************..[3703] [19]#...................[39809]
0.56 0.6 [64]****................[9554] [326]*****************...[3703] [19]#...................[39809]
0.6 0.64 [64]****................[9554] [326]******************..[3703] [19]#...................[39809]
0.64 0.68 [64]***.................[9554] [326]****************....[3703] [19]#...................[39809]
0.68 0.72 [64]***.................[9554] [326]****************....[3703] [19]#...................[39809]
0.72 0.76 [64]***.................[9554] [326]***************.....[3703] [19]#...................[39809]
0.76 0.8 [64]**..................[9554] [326]**************......[3703] [19]#...................[39809]
0.8 0.84 [64]**..................[9554] [326]*************.......[3703] [19]#...................[39809]
0.84 0.88 [64]**..................[9554] [326]************........[3703] [19]#...................[39809]
0.88 0.92 [64]**..................[9554] [326]************........[3703] [19]#...................[39809]
0.92 0.96 [64]*...................[9554] [326]***********.........[3703] [19]#...................[39809]
0.96 1 [64]*...................[9554] [326]**********..........[3703] [19]#...................[39809]
1 1.04 [64]*...................[9554] [326]*********...........[3703] [19]#...................[39809]
1.04 1.08 [64]*...................[9554] [326]********............[3703] [19]#...................[39809]
1.08 1.12 [64]*...................[9554] [326]********............[3703] [19]#...................[39809]
1.12 1.16 [64]*...................[9554] [326]********............[3703] [19]#...................[39809]
1.16 1.2 [64]*...................[9554] [326]*******.............[3703] [19]#...................[39809]
1.2 1.24 [64]#...................[9554] [326]******..............[3703] [19]#...................[39809]
1.24 1.28 [64]#...................[9554] [326]*****...............[3703] [19]#...................[39809]
1.28 1.32 [64]#...................[9554] [326]*****...............[3703] [19]#...................[39809]
1.32 1.36 [64]#...................[9554] [326]****................[3703] [19]#...................[39809]
1.36 1.4 [64]#...................[9554] [326]****................[3703] [19]#...................[39809]
1.4 1.44 [64]#...................[9554] [326]****................[3703] [19]#...................[39809]
1.44 1.48 [64]#...................[9554] [326]***.................[3703] [19]#...................[39809]
1.48 1.52 [64]#...................[9554] [326]***.................[3703] [19]#...................[39809]
1.52 1.56 [64]#...................[9554] [326]***.................[3703] [19]#...................[39809]
1.56 1.6 [64]#...................[9554] [326]**..................[3703] [19]#...................[39809]
1.6 1.64 [64]#...................[9554] [326]**..................[3703] [19]#...................[39809]
1.64 1.68 [64]#...................[9554] [326]**..................[3703] [19]#...................[39809]
1.68 1.72 [64]#...................[9554] [326]*...................[3703] [19]#...................[39809]
1.72 1.76 [64]#...................[9554] [326]*...................[3703] [19]#...................[39809]
1.76 1.8 [64]#...................[9554] [326]*...................[3703] [19]#...................[39809]
1.8 1.84 [64]#...................[9554] [326]#...................[3703] [19]#...................[39809]
1.84 1.88 [64]#...................[9554] [326]#...................[3703] [19]#...................[39809]
1.88 1.92 [64]#...................[9554] [326]#...................[3703] [19]#...................[39809]
1.92 1.96 [64]#...................[9554] [326]#...................[3703] [19]#...................[39809]
1.96 2 [64]#...................[9554] [326]#...................[3703] [19]#...................[39809]
Randomly selecting words from a list¶
Given this word list, first take a look to see what the first few lines look like:
head data/english-words.txt
a
aa
aal
aalii
aam
aardvark
aardwolf
aba
abac
abaca
Then the following will randomly sample ten words with four to eight characters in them:
mlr --from data/english-words.txt --nidx filter -S 'n=strlen($1);4<=n&&n<=8' then sample -k 10
thionine
birchman
mildewy
avigate
addedly
abaze
askant
aiming
insulant
coinmate
Randomly generating jabberwocky words¶
These are simple n-grams as described here. Some common functions are located here. Then here are scripts for 1-grams 2-grams 3-grams 4-grams, and 5-grams.
The idea is that words from the input file are consumed, then taken apart and pasted back together in ways which imitate the letter-to-letter transitions found in the word list – giving us automatically generated words in the same vein as bromance and spork:
mlr --nidx --from ./ngrams/gsl-2000.txt put -q -f ./ngrams/ngfuncs.mlr -f ./ngrams/ng5.mlr
beard
plastinguish
politicially
noise
loan
country
controductionary
suppery
lose
lessors
dollar
judge
rottendence
lessenger
diffendant
suggestional