Table 1 Average estimates and the corresponding MSE (within brackets) of two estimators
From: The estimation of the Burr-XII parameters with middle-censored data
n | Method | (0.25,0.25) | (0.5,0.5) | (0.5,0.75) | (1,0.75) | (1.25,0.5) | |||||
|---|---|---|---|---|---|---|---|---|---|---|---|
a | b | a | b | a | b | a | b | a | b | ||
10 | MLE | 1.156 | 1.095 | 1.144 | 1.147 | 1.136 | 1.081 | 1.104 | 1.136 | 1.088 | 1.112 |
(0.171) | (0.107) | (0.159) | (0.162) | (0.150) | (0.092) | (0.116) | (0.150) | (0.099) | (0.125) | ||
Bayes | 1.104 | 1.079 | 1.097 | 1.113 | 1.133 | 1.074 | 1.087 | 1.130 | 1.084 | 1.096 | |
(0.130) | (0.102) | (0.122) | (0.141) | (0.163) | (0.096) | (0.111) | (0.159) | (0.108) | (0.121) | ||
CP | 19.5% | 25.2% | 33.4% | 24.3% | 15.8% | ||||||
30 | MLE | 1.098 | 1.079 | 1.073 | 1.082 | 1.102 | 1.071 | 1.074 | 1.088 | 1.080 | 1.067 |
(0.031) | (0.032) | (0.030) | (0.033) | (0.034) | (0.039) | (0.030) | (0.036) | (0.033) | (0.037) | ||
Bayes | 1.039 | 1.036 | 1.064 | 1.072 | 1.100 | 1.049 | 1.072 | 1.080 | 1.077 | 1.037 | |
(0.034) | (0.036) | (0.032) | (0.038) | (0.039) | (0.040) | (0.036) | (0.037) | (0.034) | (0.030) | ||
CP | 15.1% | 20.2% | 29.3% | 20.1% | 13.3% | ||||||
50 | MLE | 1.018 | 1.017 | 1.008 | 1.032 | 1.061 | 1.036 | 1.052 | 1.062 | 1.022 | 1.022 |
(0.028) | (0.026) | (0.029) | (0.025) | (0.029) | (0.026) | (0.025) | (0.022) | (0.025) | (0.027) | ||
Bayes | 1.036 | 1.032 | 1.049 | 1.051 | 1.094 | 1.036 | 1.066 | 1.071 | 1.049 | 1.035 | |
(0.030) | (0.031) | (0.029) | (0.033) | (0.031) | (0.032) | (0.028) | (0.032) | (0.028) | (0.022) | ||
CP | 14. 9% | 19.7% | 29.5% | 21.4% | 14.1% | ||||||
70 | MLE | 0.990 | 0.962 | 0.997 | 1.010 | 1.031 | 0.997 | 0.982 | 1.037 | 0.985 | 0.996 |
(0.013) | (0.012) | (0.015) | (0.013) | (0.017) | (0.017) | (0.010) | (0.018) | (0.016) | (0.017) | ||
Bayes | 1.015 | 0.974 | 1.008 | 1.025 | 1.048 | 1.034 | 1.042 | 1.053 | 1.002 | 1.012 | |
(0.016) | (0.015) | (0.019) | (0.017) | (0.021) | (0.022) | (0.015) | (0.021) | (0.020) | (0.021) | ||
CP | 15.2% | 20.3% | 28.8% | 20.9% | 13.9% | ||||||
100 | MLE | 0.961 | 0.958 | 0.993 | 0.996 | 0.978 | 0.983 | 0.929 | 1.002 | 0.907 | 0.971 |
(0.010) | (0.010) | (0.009) | (0.011) | (0.009) | (0.012) | (0.008) | (0.012) | (0.013) | (0.013) | ||
Bayes | 1.001 | 0.962 | 1.012 | 1.015 | 0.998 | 0.995 | 0.980 | 1.020 | 0.980 | 0.981 | |
(0.012) | (0.013) | (0.011) | (0.013) | (0.015) | (0.014) | (0.015) | (0.016) | (0.017) | (0.016) | ||
CP | 15.0% | 20.5% | 28.9% | 21.1% | 14.5% | ||||||