Table 7.

Simulation results: proportion of replications where the maximum likelihood estimator is larger than the true value of the parameter for the log-logistic model

				1Naive estimator		TBE
λ	β	p	n	$$\hat{\lambda }>\lambda$$	$$\hat{\beta }>\beta$$	$$\hat{\lambda }>\lambda$$	$$\hat{\beta }>\beta$$
0.05	0.5	0.25	100	100%	100%	67.2%	67.7%
			500	100%	100%	53.6%	52.0%
0.05	0.5	0.50	100	100%	100%	55.4%	57.5%
			500	100%	100%	51.1%	52.0%
0.05	0.5	0.80	100	100%	100%	51.1%	53.2%
			500	100%	100%	50.8%	51.5%
1	0.5	0.25	100	100%	100%	67.7%	66.1%
			500	100%	100%	55.9%	56.1%
1	0.5	0.50	100	100%	100%	54.9%	57.2%
			500	100%	100%	53.4%	53.4%
1	0.5	0.80	100	100%	100%	55.1%	56.5%
			500	100%	100%	51.9%	52.0%
0.05	2	0.25	100	100%	100%	53.2%	55.9%
			500	100%	100%	51.8%	51.8%
0.05	2	0.50	100	100%	100%	55.0%	54.2%
			500	100%	100%	53.3%	52.2%
0.05	2	0.80	100	100%	100%	50.3%	51.5%
			500	100%	100%	53.9%	54.4%
1	2	0.25	100	100%	100%	52.7%	56.1%
			500	100%	100%	53.3%	51.0%
1	2	0.50	100	100%	100%	54.3%	56.4%
			500	100%	100%	50.1%	49.5%
1	2	0.80	100	100%	100%	52.0%	53.7%
			500	100%	100%	52.9%	55.0%

Calculations were made on the replications where there was no problem of maximization. Abbreviations : TBE truncation-based estimator.