plot(data,char,size,clr)

a5298464-03f4-4007-a3f1-56a5aa44a451 21 4 5 decimal

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

data char size clr plot k 1 data rows range r3 k el char : r4 k el size : r5 k el clr : 13 mat for data r3 r4 r5 augment 21 line :

X 1.304 1.088 0.335 0.493 1.945 1.123 1.274 0.476 2.03 1.402 3.645 1.28 0.326 0.153 0.961 0.3 1.236 2.007 0.264 0.964 201 mat :

length _X n 20 :

log vraisemblance α β x L n α β * ln * β 1 - (X i el ln i 1 n sum * + (α X i el β^i 1 n sum * - :

partial derivatives and
1rst order conditions. α β x L α diff n α / X i el (β^i 1 n sum - ≡ (0 ≡ α β x L β diff n β / X i el ln i 1 n sum + α X i el (β^(X i el ln * i 1 n sum * - ≡ (0 ≡ 21 sys

system n α / X i el (β^i 1 n sum - 0 ≡ n β / X i el ln i 1 n sum + α X i el (β^(X i el ln * i 1 n sum * - 0 ≡ 21 mat :

init α 1 ≡ β 1 ≡ 21 mat :

α β sol system init FindRoot :

α β 21 mat α β sol : 0.724606361930263 1.44400789577583 21 mat

sanity n α / X i el (β^i 1 n sum - n β / X i el ln i 1 n sum + α X i el (β^(X i el ln * i 1 n sum * - 21 mat : 0.000000017 0.000000001 - 21 mat

Weibull  log likely
probability PDF x β W β 1 el β 2 el * x β 2 el 1 - (^β 1 el x β 2 el^* - exp * (* :

X sum n / 1.1303

β 0.7246 1.444 21 mat :

i 1 X rows range Y i el X i el β W eval : for XY X Y augment : data XY o 5 black plot : 31 line

Rate of failure over vector 'X'

data x β W 2 1 sys

Weibull log vraisemblance . . . [ loglikelihood]

Two sets of conditions are required for solving the two

parameters α, β. Nicely enough, more savant Mathematicians

concluded the L(α,β,x) and the two solving conditions wrt the

data vector X. Smath spits out solution with great elegance !

]]> Golden ratio min/max

Code adapted from Valery Ochov Mathcad 11 f a b test TOL Extrema a b G 32 / b * 12 / a * - 12 / 5 sqrt * a b - (* + : y1 y2 ≥ (max in range ≡ y1 y2 ≤ (min in range ≡ x1 a b G eval : y1 x1 f eval : x2 b a G eval : y2 x2 f eval : 41 line iter 0 : iter 1000 < a b - abs TOL ≤ break test b x2 : x2 x1 : y2 y1 : x1 a b G eval : y1 x1 f eval : 51 line a x1 : x1 x2 : y1 y2 : x2 b a G eval : y2 x2 f eval : 51 line if iter iter 1 + : 21 line if while a b + 2 / 71 line :

a b + 2 / iter 21 mat

y1 y2 ≥ (max in range ≡ y1 y2 ≤ (min in range ≡ 21 sys

x f x β W eval :

ε 106 -^:

X f 0.375 1 y1 y2 ≥ ε Extrema :

X X f 21 mat 0.5523 0.5911 21 mat

Minimize Conjugate-Gradient

data char size clr plot k 1 data rows range r3 k el char : r4 k el size : r5 k el clr : 13 mat for data r3 r4 r5 augment 21 line :

init iter Minimize XY f φ β LS X XY 1 col : Y XY 2 col : n XY rows : k x β φ length 1 - : vx-> raw initial vector fit i 1 X length range vx i el X i el β f eval : for M-> Cholesky GradientMatrix j 1 k range i 1 n range M i j el X i el β φ j 1 + el eval : for for CholeskySolver LeastSquares Φ M transpose M * : d M transpose Y vx - (* : Δβ Φ 1 -^eval d * : b β Δβ + : 131 line : β 1 el init : i 1 : i iter ≤ β i 1 + el XY f φ β i el LS : i i 1 + : 21 line while β β iter el : 41 line β 31 line :

Vector Gradient ... Optimiz Symbolic
seemingly a scalar kernel  not 
recognized in program loop x β f n φ ct 1 : i 1 n range PD ct el x β f (β ct el diff : stack f(x,β) & PD V 1 el x β f : V i 1 + el PD i el : 21 line ct ct 1 + : 41 line for V 31 line :

Error stem plot for QuickPlot unicolor data Error stemX 1 data rows range : i 1 stemX rows range stem i el data i 1 el data i 2 el data i 1 el 022 mat : for i 1 stem rows 1 - range stem i el stem i el stem i 1 + (1 el 1 el 012 mat stack : for V stem 1 el : j 2 stem rows 1 - range V V stem j el stack : for V V data data rows row stack : 71 line :

L H N xd U 0 : dx H L - N / : i 1 N 1 + range U i el L dx - (dx i * + : for U 41 line :

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 :

corr Pearson correlation χ X Mean : μ Y Mean : n XY rows : 13 mat X i el χ - (Y i el μ - (* (i 1 n sum X i el χ - (2^(i 1 n sum Y i el μ - (2^(i 1 n sum * sqrt / X i el χ - (X i el β f eval μ - (* (i 1 n sum X i el χ - (2^(i 1 n sum X i el β f eval μ - (2^(i 1 n sum * sqrt / / 31 line :

correlation between [X,Y data]

correlation ... [X,fitted model]

Absolute  residuals observer
fetches β from calculated δ j 1 XY rows range Δ j el Y j el X j el β f - eval : for X Δ augment 21 line :

SSD = "Sum Square Differences" SSD Y i el X i el β f - (2^(i 1 XY rows sum :

Otherwise Pearson independent of f(x,ParameterName) x y corr n x length : xy x y * vectorize : x2 x x * vectorize : y2 y y * vectorize : n xy sum (* x sum (y sum (* - n x2 sum (* x sum (2^- (n y2 sum (* y sum (2^- (* (sqrt / 51 line :

Fit.Y ii 1 n range Fit ii el X ii el β f : for Fit 21 line :

Weibull ... infectious evolution

Weibull reference x k λ W k λ / x λ / (k λ -^* x λ / (k^- exp * :

t0 1 time :

XY 0.132 0.1 0.322 0.258 0.511 0.543 0.701 0.506 0.891 0.606 1.082 0.622 1.27 0.569 1.46 0.453 1.65 0.438 1.839 0.316 2.029 0.29 2.219 0.195 122 mat :

<= model function x β f β 1 el β 2 el * x β 2 el 1 -^* β 1 el x β 2 el^* - exp * :

in φ(x,β,f,n) -> set 'n' to last index β # el ≡

<= Gradient Vector Function x β φ x β f 2 φ :

X XY 1 col : (simply a time index] ≡ Y XY 2 col : (infectiuos evolution ≡ n XY rows : data XY o 5 black plot : 41 line

L 0 : H 5 : N 199 : 13 mat U L H N xd : 21 line

hyper robust wrt init init 0.1 112 mat transpose :

iter 5 :

algo solving for β β init iter Minimize :

assign/isolate .. β β :

Absolute  residuals δ j 1 XY rows range Δ j el Y j el X j el β f - eval : for X Δ augment 21 line :

β 0.5022 2.0003 21 mat

β 0.5022 2.0003 21 mat

corr 0.6678

FIT i 1 U rows range vy i el U i el β f eval : for U vy augment 21 line :

bar δ 0.025 BarSize :

barDev bar 1 col 1 bar 2 col * augment :

Weibull fit to Carlos data set

barDev FIT data 3 1 sys

δ 0.132 0.031 - 0.322 0.049 - 0.511 0.093 0.701 0.044 - 0.891 0.005 1.082 0.018 1.27 0.001 1.46 0.05 - 1.65 0.016 1.839 0.022 - 2.029 0.032 2.219 0.007 122 mat

1 time t0 - 3 s *

5 β f 1.8 105 -^*

jmG: 20230621