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

Table 1

Conventional moment-based parameters (𝛾₃,𝛾₄) of skew and kurtosis and their estimates (𝑔₃,𝑔₄) for the pdf in Figure 1. Each bootstrapped estimate (Estimate), associated 95% bootstrap confidence interval (95% Bootstrap C.I.), and the standard error (St. error) were based on resampling 25,000 statistics. Each statistic was based on a sample size of 𝑛=50.

Parameter	Estimate	95% Bootstrap C.I.	St. error
𝛾3=3.00	𝑔3=1.9060	(1.8955, 1.9163)	0.0053
𝛾4=21.00	𝑔4=4.7900	(4.7199, 4.8525)	0.0338