<p> plot(data,char,size,clr) </p>

a5298464-03f4-4007-a3f1-56a5aa44a451 9 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 : 31 line 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 * (* eval :

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

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 !

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