id	author	title	date	pages	extension	mime	words	sentence	flesch	summary	cache	txt
cana-6157	Asma Bouaziz	Modeling and Fitting the Alpha-Power Transformed Extended Exponential Distribution for Competing Risks: Methods and Applications	2025	14	.pdf	application/pdf	5221	255	56	(𝛼 1−𝑒𝑥𝑝(1−(1+�̂�𝑎𝑗) �̂� ) ̂ −1)) (�̂� − 1)2 − ( 𝑙𝑛 �̂�(1−𝑒𝑥𝑝(1−(1+�̂�𝑎𝑗−1) �̂� ))(𝛼 1−𝑒𝑥𝑝(1−(1+�̂�𝑎𝑗−1) �̂� ) ̂ −1) ) (�̂�−1)2 (16) 𝜕𝑃𝑗(�̂�) 𝜕�̂� = ( (1+�̂�𝑎𝑗) �̂� 𝑙𝑛(1+�̂�𝑎𝑗) (𝛼 1−𝑒𝑥𝑝(1−(1+�̂�𝑎𝑗) �̂� ) ̂ )(−𝑒𝑥𝑝(1−(1+�̂�𝑎𝑗) �̂� )) ) (�̂�−1)2 - ( (1+�̂�𝑎𝑗−1) �̂� 𝑙𝑛(1+�̂�𝑎𝑗−1) (𝛼 1−𝑒𝑥𝑝(1−(1+�̂�𝑎𝑗−1) �̂� ) ̂ )(−𝑒𝑥𝑝(1−(1+�̂�𝑎𝑗−1) �̂� )) ) (�̂�−1)2 (17) 𝜕𝑃𝑗(�̂�) 𝜕�̂̂� = ( �̂�𝑎𝑗(1+�̂�𝑎𝑗) 𝛽−1̂ (𝛼 1−𝑒𝑥𝑝(1−(1+�̂�𝑎𝑗) �̂� ) ̂ )(−𝑒𝑥𝑝(1−(1+�̂�𝑎𝑗) �̂� )) ) (�̂�−1)2 Communications on Applied Nonlinear Analysis ISSN: 1074-133X Vol 32 No. 10s (2025) 3487 https://internationalpubls.com − ( �̂�𝑎𝑗−1(1+�̂�𝑎𝑗−1) 𝛽−1̂ (𝛼 1−𝑒𝑥𝑝(1−(1+�̂�𝑎𝑗−1) �̂� ) ̂ )(−𝑒𝑥𝑝(1−(1+�̂�𝑎𝑗−1) �̂� )) ) (�̂�−1)2 (18) = (L1, L2, L3) T is given by: 𝐿1(�̂�) = ∑ 𝜐𝑗 𝑃𝑗 𝜕𝑃𝑗 𝜕�̂� (�̂�) 𝑗 ; 𝐿2(�̂�) = ∑ 𝜐𝑗 𝑃𝑗 𝜕𝑃𝑗 𝜕�̂̂� (�̂�) 𝑗 ;  𝐿3(�̂�) =∑ 𝜐𝑗 𝑃𝑗 𝜕𝑃𝑗 𝜕�̂� (𝜃) 𝑗 III.	cache/cana-6157.pdf	txt/cana-6157.txt