Journal of Probability and Statistics

Research Article

New Technique to Estimate the Asymmetric Trimming Mean

Table 1

Linear estimators.


Estimator	Estimate	Variance	RE	Ln(RE)	Bias

Beta distributions (2,4)

3G0.20	0.330061	0.034774	1.000000	0	0.003266
3G0.10	0.326579	0.034809	1.001000	0.001	0.006748
4G0.10	0.342047	0.034839	1.001880	0.00188	$-$ 0.008720
T0.10	0.342047	0.034839	1.001880	0.00188	$-$ 0.008720
P0.10	0.342047	0.034839	1.001880	0.00188	$-$ 0.008720
T0.20	0.343893	0.034875	1.002900	0.0029	$-$ 0.010566
P0.20	0.343893	0.034875	1.002900	0.0029	$-$ 0.010566
LQW_0.1250.10	0.313242	0.035167	1.011290	0.01123	0.020085
LQW_0.250.10	0.313242	0.035167	1.011290	0.01123	0.020085
4G0.20	0.357454	0.035345	1.016430	0.0163	$-$ 0.024127
LQW_0.1250.20	0.303437	0.035657	1.025380	0.02506	0.029890
LQW_0.250.20	0.291850	0.036483	1.049160	0.04799	0.041477

Gamma distribution (3,2)

T0.20	6.036901	7.783501	0.999751	$-$ 0.0002	$-$ 0.036792
3G0.10	5.942697	7.785443	1.000000	0	0.057412
T0.10	5.942697	7.785443	1.000000	0	0.057412
LQW_0.1250.10	5.942697	7.785443	1.000000	0	0.057412
3G0.20	5.845643	7.806007	1.002641	0.00264	0.154466
4G0.10	6.168469	7.810492	1.003217	0.00321	$-$ 0.168360
P0.10	6.168469	7.810492	1.003217	0.00321	$-$ 0.168360
LQW_0.1250.20	5.845643	7.806007	1.002641	0.00264	0.154466
LQW_0.250.10	6.168469	7.810492	1.003217	0.00321	$-$ 0.168360
P0.20	6.228680	7.834392	1.006287	0.00627	$-$ 0.228571
LQW_0.250.20	6.228680	7.834392	1.006287	0.00627	$-$ 0.228571
4G0.20	6.439132	7.974888	1.024333	0.02404	$-$ 0.439023

Chi-square distribution $(4)$

3G0.10	3.997780	9.828042	1.000000	0	0.002420
T0.10	3.997780	9.828042	1.000000	0	0.002420
P0.10	3.997780	9.828042	1.000000	0	0.002420
3G0.20	4.089484	9.836008	1.000811	0.00081	$-$ 0.089284
P0.20	3.881409	9.842147	1.001435	0.00143	0.118790
T0.20	3.881409	9.842147	1.001435	0.00143	0.118790
4G0.10	4.301156	9.918610	1.009215	0.00917	$-$ 0.300956
4G0.20	4.348989	9.949690	1.012378	0.0123	$-$ 0.348789
LQW_0.1250.10	3.345020	10.257297	1.043677	0.04275	0.655180
LQW_0.250.10	3.345020	10.257297	1.043677	0.04275	0.655180
LQW_0.1250.20	2.791903	11.288018	1.148552	0.1385	1.208297
LQW_0.250.20	2.791903	11.288018	1.148552	0.1385	1.208297

Burr distribution (3,1)

3G0.20	0.494108	0.278845	1.000000	0	0.006350
P0.20	0.494108	0.278845	1.000000	0	0.006350
3G0.10	0.492520	0.278868	1.000081	0.000081	0.007938
T0.10	0.492520	0.278868	1.000081	0.000081	0.007938
P0.10	0.492520	0.278868	1.000081	0.000081	0.007938
T0.20	0.462763	0.280226	1.004951	0.004939	0.037694
4G0.10	0.541519	0.280491	1.005902	0.005885	$-$ 0.041061
4G0.20	0.546247	0.280902	1.007375	0.007348	$-$ 0.045790
LQW_0.1250.10	0.388761	0.291281	1.044597	0.043631	0.111697
LQW_0.250.10	0.388761	0.291281	1.044597	0.043631	0.111697
LQW_0.1250.20	0.314296	0.313462	1.124141	0.117019	0.186162
LQW_0.250.20	0.314296	0.313462	1.124141	0.117019	0.186162

Pareto distribution (3,1)

3G0.20	1.513229	5.210438	1.000000	0	$-$ 0.013318
4G0.20	1.513229	5.210438	1.000000	0	$-$ 0.013318
T0.20	1.513229	5.210438	1.000000	0	$-$ 0.013318
3G0.10	1.622767	5.225354	1.002863	0.00286	$-$ 0.122856
4G0.10	1.622767	5.225354	1.002863	0.00286	$-$ 0.122856
T0.10	1.622767	5.225354	1.002863	0.00286	$-$ 0.122856
P0.10	1.370864	5.226914	1.003162	0.00316	0.129048
p0.20	1.099740	5.370398	1.030700	0.03024	0.400172
LQW_0.1250.10	0.919826	5.546760	1.064548	0.06255	0.580086
LQW_0.250.10	0.919826	5.546760	1.064548	0.06255	0.580086
LQW_0.1250.20	0.728119	5.805925	1.114287	0.10821	0.771793
LQW_0.250.20	0.775311	5.735306	1.100734	0.09598	0.724600

Weibull distribution (1,3)

3G0.10	2.999831	9.738460	1.000000	0	0.000277
P0.10	2.999831	9.738460	1.000000	0	0.000277
3G0.20	3.074395	9.743978	1.000567	0.00057	$-$ 0.074287
P0.20	3.074395	9.743978	1.000567	0.00057	$-$ 0.074287
4G0.10	3.253236	9.802534	1.006579	0.00656	$-$ 0.253128
T0.10	2.765150	9.793665	1.005669	0.00565	0.234958
4G0.20	3.328679	9.846419	1.011086	0.01103	$-$ 0.328572
T0.20	2.618965	9.883730	1.014917	0.01481	0.381143
LQW_0.1250.10	2.346914	10.165121	1.043812	0.04288	0.653193
LQW_0.250.10	2.346914	10.165121	1.043812	0.04288	0.653193
LQW_0.1250.20	1.692180	11.449135	1.175662	0.16183	1.307928
LQW_0.250.20	1.692180	11.449135	1.175662	0.16183	1.307928

Skewed-normal distribution

3G0.20	2.593322	0.214400	1.000000	0	0.003977
T0.20	2.593322	0.214400	1.000000	0	0.003977
LQW_0.1250.20	2.593322	0.214400	1.000000	0	0.003977
3G0.10	2.586861	0.214494	1.000434	0.00043	0.010438
T0.10	2.586861	0.214494	1.000434	0.00043	0.010438
LQW_0.1250.10	2.586861	0.214494	1.000434	0.00043	0.010438
P0.10	2.623642	0.215079	1.003163	0.00316	$-$ 0.026343
p0.20	2.627732	0.215311	1.004246	0.00424	$-$ 0.030432
LQW_0.250.10	2.552086	0.216429	1.009461	0.00942	0.045214
4G0.10	2.661124	0.218458	1.018926	0.01875	$-$ 0.063825
4G0.20	2.697760	0.224477	1.046999	0.04593	$-$ 0.100461
LQW_0.250.20	2.495980	0.224650	1.047806	0.0467	0.101319