83b9d79c-44a7-4939-989c-06b87ba1af1d 9 4 5 decimal

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

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