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

Table 4

Monte Carlo simulation results for the AT-W distribution using Set III values (α = 2.0 and λ = 1.2).

Parameters	n	Set III
		MLE	AB	MSE	RMSE
	25	2.1311	0.1311	0.1438	0.3792
	50	2.0523	0.0523	0.0523	0.2286
	100	2.0230	0.0230	0.0236	0.1536
	200	2.0092	0.0092	0.0120	0.1095
	300	2.0088	0.0088	0.0086	0.0927
	400	2.0076	0.0076	0.0063	0.0794
	500	2.0048	0.0048	0.0049	0.0700
	600	2.0038	00038	0.0042	0.0648
	700	2.0022	0.0022	0.0030	0.0548
	25	1.2255	0.0255	0.0198	0.1407
	50	1.2082	0.0082	0.0086	0.0927
	100	1.2056	0.0056	0.0041	0.0640
	200	1.2046	0.0046	0.0022	0.0469
	300	1.2030	0.0030	0.0013	0.0361
	400	1.2015	0.0015	0.0011	0.0332
	500	1.2005	0.0005	0.0008	0.0283
	600	1.2004	0.0004	0.0006	0.0245
	700	1.2003	0.0003	0.0005	0.0223