Research Article

Characterizing Tukey and -Distributions through 𝐿 -Moments and the 𝐿 -Correlation

Table 4

Cholesky decompositions for the Conventional moment procedure.
(a)

𝑎 1 1 = 1 𝑎 1 2 = 0 . 7 2 6 𝑎 1 3 = 0 . 7 2 2 𝑎 1 4 = 0 . 8 8 1
0 𝑎 2 2 = 0 . 6 8 7 𝑎 2 3 = 0 . 2 7 7 𝑎 2 4 = 0 . 1 1 2
00 𝑎 3 3 = 0 . 6 3 3 𝑎 3 4 = 0 . 0 6 2
000 𝑎 4 4 = 0 . 4 5 5

(b)

𝑎 1 1 = 1 𝑎 1 2 = 0 . 4 2 4 𝑎 1 3 = 0 . 5 2 1 𝑎 1 4 = 0 . 6 2 6
0 𝑎 2 2 = 0 . 9 0 6 𝑎 2 3 = 0 . 2 1 3 𝑎 2 4 = 0 . 2 7 5
00 𝑎 3 3 = 0 . 8 2 7 𝑎 3 4 = 0 . 0 2 5
000 𝑎 4 4 = 0 . 7 2 9