A Method for Simulating Burr Type III and Type XII Distributions through 𝐿-Moments and 𝐿-Correlations

Table 5

𝐿-moment-based parameters of 𝐿-mean (𝜆₁), 𝐿-scale (𝜆₂), 𝐿-skew (𝜏₃), and 𝐿-kurtosis (𝜏₄) along with their corresponding values of shape parameters (𝑐 and 𝑘) for the four distributions (dashed curves) in Figure 2 (Panel b).

Distribution	𝜆1	𝜆2	𝜏3	𝜏4	𝑐	𝑘
1	0.441134	0.221816	0.387355	0.233548	1.227122	3.417227
2	0.349660	0.226233	0.464102	0.226497	−2.944030	0.126960
3	0.643787	0.182777	0.169925	0.150375	2.498521	2.913452
4	0.936479	0.085223	0.0	0.166667	−13.875566	0.562179