The Arctan-X Family of Distributions: Properties, Simulation, and Applications to Actuarial Sciences

Table 3

Monte Carlo (MC) simulation results for the AT-W distribution using Set II values (α = 0.8 and λ = 1.5).

Parameters	n	Set I
		MLE	AB	MSE	RMSE
	25	0.8540	0.0540	0.0242	0.1556
	50	0.8231	0.0231	0.0084	0.0916
	100	0.8147	0.0147	0.0040	0.0632
	200	0.8072	0.0072	0.0019	0.0436
	300	0.8034	0.0034	0.0013	0.0361
	400	0.8026	0.0026	0.0007	0.0265
	500	0.8023	0.0023	0.0006	0.0245
	600	0.8020	0.0020	0.0005	0.0223
	700	0.8018	0.0018	0.0004	0.0200
	25	1.6155	0.1155	0.2185	0.4674
	50	1.5485	0.0485	0.0912	0.3020
	100	1.5333	0.0333	0.0450	0.2121
	200	1.5130	0.0130	0.0180	0.1342
	300	1.5081	0.0081	0.0150	0.1225
	400	1.5044	0.0044	0.0084	0.0916
	500	1.5040	0.0040	0.0072	0.0848
	600	1.5037	0.0037	0.0058	0.0762
	700	1.5021	0.0021	0.0042	0.0648