<content> Stem Construction Utility </content>

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Core component of the stem style P v replicate k 1 : i 1 v length range P i el 1 ≡ continue j 1 P i el range T k j + el v i el : for k k P i el + : 21 line if for T 31 line :

Stem construction vy stem N vy length : i 1 N range q i el 3 : q N el 2 : 21 line for 11 line i 1 N range v i el i : for i 1 N range S 3 i * el vy i el : for u q v replicate : V u S augment : V V 3 V rows 12 submatrix : 71 line :

E.g. for a logistic distribution with parameters m and b,
the cumulative distribution function is:

F(x) = 1/(1+exp(-(x-m)/b)) ... so the inverse is
G(x) = m - b*log(1/y - 1)

A random sample can then be drawn with
gen y = `m' - `b'*log(1/uniform() - 1)
(where `m' and `b' are locals containing the parameters m and b)

t0 1 time :

x m b q 11 x m - (- b / exp + / :

y x m b q ≡ x solve maple m 1 - y + y / ln b * -

# uniform size 1100 Random.N ≡

L 1 : S 0.5 : 12 mat

Number of individual samples to collectNumber of data points in each sample NSamples 25 : SSize 1000 : 21 sys

a 0.95 : b 1.05 : 12 mat

Means ε 1 : xRnd 1 SSize 0100 Random.N * ε + : SSize L S rlogis L 1 xRnd / ln vectorize S * - : rnd SSize L S rlogis : count 1 : i 1 NSamples range xRnd 15 / SSize 110 Random.N * : SSize L S rlogis L 1 xRnd / ln vectorize S * - : rnd SSize L S rlogis : LocalLogis count el rnd Mean b a - 2 / + : count count 1 + : 61 line for LocalLogis 71 line :

Means Means eval :

Means Min Means Max 21 mat 0.982 1.021 21 mat

Success a Means i el ≤ (Means i el b ≤ (& i 1 NSamples sum :

Prob Success NSamples / : 1.000

Success 25

Random Means stem :

b a Random 3 1 sys

1 time t0 - 4.1 s *

<content> Scale(M,Low,High) </content>

M Low High Scale High Low - (M M Min - M Max M Min - 1012 -^+ / (* Low + :

m λ s Logistic m λ - s / - exp s 1 m λ - s / - exp + (2^* / :

x 1 0.5 Logistic

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

Randomize a function

To regenerate new set of randomized function,
click in any active gray region => press F9.
"level" = max level of random excursion...± level.

Random(n)=> Uniform ...  -1 < rnd < 1 n level rnd level n Random * level 2 / - 11 line :

x f span level populate randomize x 5 - span 5 - 1 populate / + range : i 1 x rows range y i el x i el f : for x y x rows level rnd + augment x y augment 21 mat 31 line :

XY 1 el noisy ≡ XY 2 el clean ≡ 21 mat

x f x 1 0.5 Logistic :

level 0.0625 :

XY x f 5 level 9.9 randomize :

a b c spec . 8 black 13 mat : data XY 1 el a b c spec pts : 21 line

XY 1 el rows 100

2 periods of noisy sine

data XY 2 el 2 1 sys

Yrnd XY 1 el 2 col :

1 time t0 - 4.4 s *

Yrnd Yrnd 0.9 + :

λ is the location parameters > 0 is a scale parameter m λ s Logistic m λ - s / - exp s 1 m λ - s / - exp + (2^* / :

Yrnd Min Yrnd Max 21 mat 0.873 1.416 21 mat

L 1 : S 0.25 : 12 mat

Number of individual samples to collectNumber of data points in each sample NSamples 25 : SSize 1000 : 21 sys

a 0.95 : b 1.05 : 12 mat

LocalLogis Means Success Clear 1

Means count 1 : i 1 NSamples range Logis Yrnd : LocalLogis count el Logis Mean b a - 2 / + : count count 1 + : 31 line for LocalLogis 31 line :

x L S Logistic

Means Means eval :

Success a Means i el ≤ (Means i el b ≤ (& i 1 NSamples sum :

Means Min Means Max 21 mat 1.0509 1.0509 21 mat

Prob 1 Success NSamples / * : 0.000

Success 0

1 time t0 - 5.1 s *

data