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

Table 2

Monte Carlo simulation results for the AT-W distribution using Set I values (α = 5.0 and λ = 4.0).

Parameters	n	Set I
		MLE	AB	MSE	RMSE
	25	5.2646	0.2646	0.7854	0.8862
	50	5.1632	0.1632	0.4005	0.6328
	100	5.0704	0.0704	0.1196	0.3458
	200	5.0280	0.0280	0.0701	0.2648
	300	5.0196	0.0196	0.0515	0.2269
	400	5.0145	0.0145	0.0351	0.1873
	500	5.0122	0.0122	0.0285	0.1688
	600	5.0091	0.0091	0.0252	0.1587
	700	5.0072	0.0072	0.0221	0.1487
	25	4.0193	0.0193	0.0329	0.1813
	50	4.0101	0.0101	0.0150	0.1225
	100	4.0069	0.0069	0.0072	0.0848
	200	4.0039	0.0039	0.0038	0.0616
	300	4.0026	0.0026	0.0023	0.0480
	400	4.0017	0.0017	0.0020	0.0447
	500	4.0015	0.0015	0.0015	0.0387
	600	4.0013	0.0012	0.0012	0.0346
	700	4.0011	0.0011	0.0011	0.0332