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

Table 4

Conventional moment based parameters of the mean (𝜇), standard deviation (𝜎), skew (𝛾₃), and kurtosis (𝛾₄) along with their corresponding values of shape parameters (𝑐 and 𝑘) for the four distributions (dashed curves) in Figure 2 (Panel a).

Distribution	𝜇	𝜎	𝛾3	𝛾4	𝑐	𝑘
1	0.306182	0.362801	4.221159	59.454545	1.097740	4.481719
2	0.139427	0.263634	2.828427	12.0	−5.542062	0.027237
3	0.415523	0.242125	1.139547	2.4	2.025127	5.374401
4	0.937510	0.139248	0.0	1.2	−15.776368	0.540152