id	author	title	date	pages	extension	mime	words	sentence	flesch	summary	cache	txt
cana-4617	A. A. A-Rahman, I. B. Abdul-Moniem, M. B. Moemen	Recurrence Relations for Moments of Generalized Order Statistics from Area-biased Rayleigh Distribution and its Characterization	2025	16	.pdf	application/pdf	5317	313	79	[1 − (�̅�(𝑧)) 𝑚+1 ] 𝑟−1 𝑑𝑧 = 𝐶𝑟−1 ∑ (𝑟−1 𝑤 )(−1)𝑤𝑟−1 𝑤=0 (𝑚 + 1)𝑟−1(𝑟 − 1)! − 𝐸[𝑍𝑗(𝑟 − 1, 𝑛, 𝑚, 𝑘)] = 𝑗𝛽2 2𝛾𝑟 {𝐸[𝑍𝑗−2(𝑟, 𝑛, 𝑚, 𝑘)] + 𝛽2𝐸[𝑍𝑗−4(𝑟, 𝑛, 𝑚, 𝑘)]} if and only if �̅�(𝑧) = (1 + 𝑧2 𝛽2 ) 𝒆𝒙𝒑 (− 𝑧2 𝛽2 ) (24) Proof: The necessity part follows directly from equation (17).	cache/cana-4617.pdf	txt/cana-4617.txt