Table 4.

Simulation results: estimations of bias and mean squared error for the log-logistic model

						Naive estimator		TBE
					$$\hat{\lambda }$$		$$\hat{\beta }$$		$$\hat{\lambda }$$		$$\hat{\beta }$$
λ	β	p	n	BIAS	MSE	BIAS	MSE	BIAS	MSE	BIAS	MSE	NPM
0.05	0.5	0.25	100	6.45	44	0.384	0.16	0.258	0.25	0.041	0.008	217
			500	6.33	40	0.372	0.14	0.043	0.01	0.005	0.001	52
0.05	0.5	0.50	100	1.05	1.2	0.319	0.108	0.045	0.012	0.020	0.006	22
			500	1.02	1.1	0.308	0.096	0.009	0.001	0.003	0.001	0
0.05	0.5	0.80	100	0.165	0.031	0.195	0.041	0.008	0.001	0.008	0.004	0
			500	0.158	0.026	0.189	0.036	0.001	<0.001	0.001	<0.001	0
1	0.5	0.25	100	129	17533	0.383	0.15	5.06	87	0.042	0.008	207
			500	127	16217	0.374	0.14	1.01	6	0.008	0.001	41
1	0.5	0.50	100	21.0	467	0.317	0.106	0.93	5.0	0.019	0.006	43
			500	20.5	426	0.308	0.096	0.20	0.6	0.004	0.001	0
1	0.5	0.80	100	3.31	12	0.201	0.044	0.209	0.55	0.016	0.005	0
			500	3.17	10	0.190	0.037	0.037	0.09	0.002	<0.001	0
0.05	2	0.25	100	0.150	0.022	1.06	1.2	<0.001	0.001	0.08	0.085	4
			500	0.149	0.022	1.04	1.1	-0.001	<0.001	0.01	0.018	0
0.05	2	0.50	100	0.079	0.006	0.932	0.94	<0.001	<0.001	0.06	0.094	5
			500	0.078	0.006	0.903	0.83	<0.001	<0.001	0.01	0.017	0
0.05	2	0.80	100	0.035	0.001	0.665	0.50	<0.001	<0.001	0.03	0.078	0
			500	0.035	0.001	0.649	0.43	<0.001	<0.001	0.01	0.013	0
1	2	0.25	100	2.99	9.0	1.07	1.2	0.024	0.57	0.08	0.089	0
			500	2.98	8.9	1.04	1.1	-0.028	0.20	0.01	0.020	0
1	2	0.50	100	1.57	2.49	0.943	0.96	0.007	0.19	0.063	0.095	1
			500	1.56	2.45	0.896	0.82	-0.013	0.04	0.004	0.018	0
1	2	0.80	100	0.702	0.50	0.668	0.50	0.004	0.042	0.045	0.072	0
			500	0.693	0.48	0.648	0.43	0.004	0.007	0.015	0.013	0

The mean squared error formula is $\text{MSE}\left(\hat{\lambda }\right)=\text{Var}\left(\hat{\lambda }\right)+{\left(\text{BIAS}\right(\hat{\lambda }\left)\right)}^2$. Calculations were made on the replications where there was no problem of maximization. In the last column appear the number of problems of maximization for the truncation-based approach. There was no problem of maximization for the naive approach. Abbreviations : TBE truncation-based estimator, MSE mean squared error, NPM number of maximization problems.