484bcfeb-969a-41c1-b55e-c1ed2940a24b 16 3 5 auto

&[DATE] &[TIME] - &[FILENAME]

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 :

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 :

Core component of the stem style P v replicate Mathcad 8 Pro. Treasury 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 41 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 Sy 3 i * el vy i el : for u q v replicate : V u Sy augment : V V 3 V rows 12 submatrix : 71 line :

L 1 : S 0.5 : 12 mat

Number of individual samples to collect
Number of data points in each sample NSamples 50 : SSize 200 : 21 sys

a 0.95 : b 1.05 : 12 mat

Means λ 10 : count 1 : i 1 NSamples range xRnd 2 λ / SSize 1 λ 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 + : 51 line for LocalLogis 41 line :

Means Means :

Means Min Means Max 21 mat 0.951 1.063 21 mat

rnd Means Means Min Means Max Scale :

μ Means Mean : 0.998

n Means rows :

i 1 n range P i el 3 : P n el 2 : 21 line for i 1 n range v i el i : for i 1 v length range Y 3 i * el rnd i el μ - : for 31 line

u P v replicate : V u Y augment : V V 3 V rows range 12 range el : 31 line

Logistic random noise

sort(rnd)
histogram N 100 rnd * Ceil sort : H N histogram : 21 sys

H N histogram :

Tail end Logistic histogram. In this Smath document, we offer no suggestion wrt the possible histogram distribution.

H 0.0001 BarSize

The UniformDistribution [min, max] , commonly referred to

as the rectangular distribution, characterizes a random variable

whose value is everywhere equally likely. An example of a

uniformely distributed random variable is the location of a

point chosen randomly on a line from min to max.

The LogisticDistribution [m, b] is frequently used in place of the

NormalDistribution when a distribution with longer tails is desired.

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Uniform

x U 0 x 2.5 ≤ 15 2.5 - / 2.5 x ≤ (x 5 ≤ (& 0 cases 0 x 4 ≤ 1104 - / 4 x ≤ (x 10 ≤ (& 0 cases 0 x 12 ≤ 11512 - / 12 x ≤ (x 15 ≤ (& 0 cases 31 sys :

u 2.5 x ≤ (x 5 ≤ (* : v 4 x ≤ (x 10 ≤ (* : w 12 x ≤ (x 15 ≤ (* : 31 line

Uniform x U 1 el u / x U 2 el v / x U 3 el w / 31 sys :

Uniform

Dlogisitic

λ s x Dlogis x λ - s / (- exp s 1 x λ - s / (- exp + (2^* / :

9 3 x Dlogis 9 4 x Dlogis 6 2 x Dlogis 2 1 x Dlogis 4 1 sys

In probability theory and statistics, the logistic distribution is a continuous probability distribution. Its cumulative distribution function is the logistic function, which appears in logistic regression and feedforward neural networks. It resembles the normal distribution in shape but has heavier tails (higher kurtosis). The Tukey lambda distribution can be considered a generalization of the logistic distribution since it adds a shape parameter, λ, and corresponds to the logistic distribution when λ is zero.