An improved generalized class of estimators for population variance using auxiliary variables

Figures & data

Table 1. PRE of various estimators with respect to $S_y^2$

Estimators	PREs
	Population I	Population II
$s_y^2$	100.0000	100.0000
tN	848.7573	698.2471
tM	848.7573	698.2471
t1	848.7573	698.2471
T	876.6598	716.6599

Table 2. Comparison of proposed estimator t with other existing estimators for Population-I

ρ	N	Average percent relative efficiency (PRE)
		$s_y^2$	tN	tM	t1	t
0.5	40	100.0000	112.0037	111.6313	110.9877	117.5637
	50	100.0000	112.1265	111.5847	110.9795	116.5967
	60	100.0000	112.1866	111.5948	110.9865	115.847
0.6	40	100.0000	122.3532	121.7895	122.9326	128.3793
	50	100.0000	122.5582	121.7388	122.9584	127.4171
	60	100.0000	122.6414	121.7331	122.9711	126.6652
0.8	40	100.0000	179.4806	177.6442	177.4084	189.413
	50	100.0000	180.2122	177.5656	177.5064	188.5566
	60	100.0000	180.3817	177.3901	177.3211	187.7472

Table 3. Comparison of proposed estimator t with other existing estimators for Population-II

ρ	N	Average per cent relative efficiency (PRE)
		$s_y^2$	tN	tM	t1	t
0.5	40	100.0000	104.493	104.2726	100.7379	109.7692
	50	100.0000	104.557	104.2354	100.6977	108.8092
	60	100.0000	104.5891	104.2507	100.6683	108.0547
0.6	40	100.0000	108.471	108.1663	106.4562	113.8899
	50	100.0000	108.5663	108.1228	106.434	112.9245
	60	100.0000	108.6153	108.1362	106.4296	112.1738
0.8	40	100.0000	133.0232	132.2563	134.1661	139.6054
	50	100.0000	133.3169	132.2032	134.2187	138.6565
	60	100.0000	133.4178	132.1748	134.2144	137.8979