An Efficient Estimation of the Mean Residual Life Function with Length-Biased Right-Censored Data

Table 1

Simulation results for nonparametric estimators based on 1000 replications.

𝑡	𝑚(𝑡)	𝑚(𝑡)			𝑚(𝑡)
		Bias	SE	MSE	Bias	SE	MSE
𝑛=100,𝐶∼Un(0,5)
0.2	0.4	51	28	34	2	29	8
0.4	0.3	50	21	30	0	20	4
0.6	0.2	50	16	28	0	15	2
0.8	0.1	50	14	27	0	11	1
𝑛=200,𝐶∼Un(0,5)
0.2	0.4	51	20	30	1	20	4
0.4	0.3	51	14	28	1	14	2
0.6	0.2	50	11	26	0	11	1
0.8	0.1	50	7	25	0	7	1
𝑛=100,𝐶∼Un(0,5/3)
0.2	0.4	49	32	35	1	30	9
0.4	0.3	49	28	31	1	22	5
0.6	0.2	48	29	31	0	17	3
0.8	0.1	45	56	51	0	12	1
𝑛=200,𝐶∼Un(0,5/3)
0.2	0.4	50	21	30	1	21	5
0.4	0.3	50	16	28	0	15	2
0.6	0.2	50	15	28	1	12	1
0.8	0.1	51	15	28	1	8	1
𝑛=100,𝐶∼Un(0,1)
0.2	0.4	49	62	62	2	32	10
0.4	0.3	53	233	572	−2	26	7
0.6	0.2	37	160	268	5	21	5
0.8	0.1	107	1733	30130	−1	15	2
𝑛=200,𝐶∼Un(0,1)
0.2	0.4	49	24	30	2	22	5
0.4	0.3	50	43	43	2	19	4
0.6	0.2	48	26	30	−2	14	2
0.8	0.1	53	134	208	−1	11	1

Notes for the numerical results based on 1000 replications in Table 1:
(1) Bias = the empirical bias × 10³;
(2) SE = the empirical standard deviation × 10³;
(3) MSE = the empirical mean square error × 10⁴.