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

Table 2

𝐿-moment-based parameters (𝜏₃,𝜏₄) of 𝐿-skew and 𝐿-kurtosis and their estimates (𝓉₃,𝓉₄) 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
𝜏3=0.3536	𝓉3=0.3455	(0.3445, 0.3465)	0.0005
𝜏4=0.2020	𝓉4=0.1965	(0.1955, 0.1975)	0.0005