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

Table 13

Correlation results for the conventional product moment-based (Pearson) correlations.

Parameter	Estimate	95% Bootstrap C.I.	St. error	RB%
		𝑛=25
𝜌12=0.80	0.8252	(0.8239, 0.8266)	0.00220	3.15
𝜌13=0.75	0.7910	(0.7899, 0.7922)	0.00155	5.47
𝜌14=0.60	0.6467	(0.6452, 0.6481)	0.00124	7.78
𝜌23=0.70	0.7125	(0.7110, 0.7141)	0.00161	1.79
𝜌24=0.50	0.5167	(0.5148, 0.5185)	0.00132	3.34
𝜌34=0.40	0.4117	(0.4094, 0.4137)	0.00131	2.93
		𝑛=1000
𝜌12=0.80	0.8026	(0.8025, 0.8031)	0.00038	0.33
𝜌13=0.75	0.7547	(0.7545, 0.7551)	0.00034	0.63
𝜌14=0.60	0.6044	(0.6040, 0.6047)	0.00026	0.73
𝜌23=0.70	0.7003	(0.7001, 0.7006)	0.00026	0.04
𝜌24=0.50	0.5007	(0.5004, 0.5010)	0.00021	0.14
𝜌34=0.40	0.4003	(0.4000, 0.4006)	0.00020	—