Table 3.

Simulation results. Proportions of rejection of three test statistics for length-biased data based on n₁ = 50 and n₂ = 150 and with 5000 simulations

X1 ~ Weibull(2,1), $X_2\sim \text{Weibull}(2,1/\sqrt{\beta })$
β	Cen1%	Cen2%	Proposed test	Prop. of rejection	Prop. of rejection
			Prop. of rejection	Truncation logrank	Standard Logrank
			$T_1^{\ast }$	TLT	TLR
No censoring
1	0%	0%	0.049	0.051	0.048
1.2	0%	0%	0.317	0.205	0.274
1.4	0%	0%	0.749	0.528	0.709
0.8	0%	0%	0.345	0.262	0.391
0.6	0%	0%	0.963	0.870	0.975
Same censoring distributions SC1 = SC2
1	20%	20%	0.052	0.051	0.051
1.2	20%	18%	0.254	0.150	0.205
1.4	20%	17%	0.659	0.423	0.608
0.8	20%	23%	0.288	0.220	0.327
0.6	20%	26%	0.936	0.778	0.947
1	40%	40%	0.051	0.052	0.051
1.2	40%	36%	0.263	0.124	0.215
1.4	40%	34%	0.591	0.330	0.518
0.8	40%	43%	0.307	0.200	0.333
0.6	40%	48%	0.889	0.681	0.887
Different censoring distributions SC1 ≠ SC2
1	20%	6%	0.049 (0.053)	0.051	0.056
1.2	20%	5%	0.282 (0.296)	0.164	0.297
1.4	20%	5%	0.674 (0.694)	0.450	0.700
0.8	20%	6%	0.269 (0.283)	0.230	0.258
0.6	20%	7%	0.910 (0.930)	0.779	0.909
1	40%	10%	0.047 (0.052)	0.049	0.084
1.2	40%	9%	0.259 (0.275)	0.143	0.389
1.4	40%	9%	0.642 (0.663)	0.381	0.761
0.8	40%	12%	0.210 (0.250)	0.202	0.151
0.6	40%	13%	0.843 (0.854)	0.696	0.768