<p> Utilities </p>

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<p> Utilities </p>

M Min Max Scale Max Min - (M M min - M max M min - 106 -^+ / (* Min + :

Bar plot unicolor style, bar width user. data dt BarSize v data 2 col : t v bar t dt - 0 t dt - v t dt + v t dt + 042 mat : j 1 data rows range j 1 ≡ B data j 1 el data j 2 el bar : B B data j 1 el data j 2 el bar stack : if 11 line for B 41 line :

N histogram value table count k 1 : j k table rows range table j el value ≡ index k el j : k k 1 + : 21 line index k el 0 : if for index rows 31 line : i 1 N max range x i el i : count i el i N count : 21 line for x count augment 31 line :

Create normal random Quick/Simple

n 200 :

bias 1 - :

Ω 10 :

Unform ...  -1 < rnd < 1 n rnd μ n 11 line : Ω μ Random * 21 line :

normal noise from CLT
Central Limit Theorem N1 n rnd Floor : N2 n rnd Ceil : N N1 N2 + bias + : 31 sys

idx 1 n range :

½noise idx N 1 - 1 Scale augment :

This Smath document produces an attractive noise distribution. It may not be suitable for specific experiments, whereas the noise is of 'normal distribution'. If the histogram turns red, F9 for a new attempt. Red H "index undefined" indicates some missing value(s) in sorted 'N'... count(value,vector)

½noise 0.001 BarSize

μ N Mean : σ N StdDev : 21 mat 8.745 3.8827 21 mat

N N sort : H N histogram : 21 line

solving user sigma s 5 :

h N Max Ceil N Min Floor - H rows / : λ n h * : 21 mat 120021 mat

x Δ λ x μ σ pdf.Normal * λ x μ s pdf.Normal * - :

H 1229313495106167188179281020111812121317148157165173182182 mat

myσ x Δ x σ s μ + solve : 4.3623 13.1277 21 mat

Σ λ σ μ σ pdf.Normal * :

sigma σ Σ . 16 black 15 mat :

Here, demo solving for s > native σ

Central Limit Theorem: confirmed

H 0.125 BarSize λ x μ σ pdf.Normal * myσ 1 el 20 myσ 1 el 4 - 2 2 mat myσ 2 el 20 myσ 2 el 4 - 2 2 mat sigma 5 1 sys

sanity check myσ Δ vectorize 1107 -^* - 3107 -^* 21 mat

Filling a statistical region [PDF]

t0 1 time :

Prepare the project

Construct the project

x f λ x μ σ pdf.Normal * :

N 1000 :

data spec pts i 1 data rows range p i el a b c spec : for v p 1 el : Unest 'p' j 2 p rows range v v p j el stack : for data v augment 51 line :

xmin myσ 1 el : xmax myσ 2 el : 12 mat ymin 0 : ymax 20 : 12 mat 21 line

space_x xmax xmin - (: space_y ymax ymin - (: 21 line

A function that tests an arbitrary point 
for its membership in the critical region. x y Test y x f ≤ (x xmax ≤ (* :

PDF x 10 - 30 9.9 - range : i 1 x rows range y i el x i el f eval : 11 line for x y augment 31 line :

A routine that finds an array of N random 
pairs in the critical region. Pts i 1 N range x 1 Random space_x * xmin + 1 el : y 1 Random space_y * ymin + 1 el : 1 x y Test - x 1 Random space_x * xmin + 1 el : y 1 Random space_y * ymin + 1 el : 21 line while P i 1 el x : P i 2 el y : 51 line for P 21 line :

a b c spec . 12 #808080 13 mat :

fill Pts a b c spec pts :

Domain

Xmin xmin 20 xmin 0.25 - 22 mat :

Xmax xmax 20 xmax 0.25 - 22 mat :

plot fill PDF Xmin Xmax 41 sys :

1 time t0 - 20.5 s *

Filling user solved 'σ' PDF region ... You can have region 'hatch' ... not offered. Black dot is the native 'σ' from random PDF.

plot μ 30 μ 10 - 2 2 mat sigma 3 1 sys