International Scholarly Research Notices / 2012 / Article / Tab 1 / Research Article
Bayesian Estimation for Burr Distribution Type III Based on Trimmed Samples Table 1 The maximum likelihood estimator, the standard deviation, and covariance of the Burr distribution with two parameter under doubly censored sample when (a) (
,
), (b) (
,
), (c) (
,
), (d) (
,
).
(a)
MLE Standard deviation MLE Standard deviation 5 4.619 3.689 7.841 4.341 58.814 10 7 2 4.534 3.524 4.672 4.172 50.042 9 4.338 3.308 4.722 3.202 22.784 10 6.874 3.874 6.654 4.154 66.589 20 15 2 6.483 2.483 6.439 3.939 64.752 18 6.147 3.147 6.307 3.807 41.058 20 6.498 3.498 6.802 4.302 74.941 40 30 3 5.384 3.384 6.471 3.971 62.603 38 5.287 2.287 5.629 3.129 39.913 30 5.692 2.692 6.794 4.294 62.054 60 45 3 5.542 2.542 6.678 4.178 47.829 58 5.201 2.201 5.489 2.989 16.475 40 5.448 2.448 6.824 4.324 78.475 80 65 5 5.707 2.707 6.671 4.171 66.942 78 5.334 2.334 5.391 2.891 11.313 50 6.689 3.689 6.841 4.341 58.814 100 75 5 6.524 3.524 6.672 4.172 50.042 98 6.308 3.308 5.702 3.202 30.784
(b)
MLE Standard deviation MLE Standard deviation 5 6.689 3.689 6.841 4.341 58.814 10 7 2 6.524 3.524 6.672 4.172 50.042 9 6.308 3.308 5.702 3.202 30.784 10 6.874 3.874 6.654 4.154 66.589 20 15 2 6.483 3.483 6.439 3.939 64.752 18 6.147 3.147 6.307 3.807 41.058 20 6.498 3.498 6.802 4.302 74.941 40 30 3 6.384 3.384 6.471 3.971 62.603 38 5.287 2.287 5.629 3.129 39.913 30 5.692 2.692 6.794 4.294 62.054 60 45 3 5.542 2.542 6.678 4.178 47.829 58 5.201 2.201 5.489 2.989 16.475 40 5.448 2.448 6.824 4.324 78.475 80 65 5 5.707 2.707 6.671 4.171 66.942 78 5.334 2.334 5.391 2.891 11.313 50 6.689 3.689 6.841 4.341 58.814 100 75 5 6.524 3.524 6.672 4.172 50.042 98 6.308 3.308 5.702 3.202 30.784
(c)
MLE Standard deviation MLE Standard deviation 5 5.952 2.952 5.159 3.159 69.043 10 7 2 5.712 2.712 4.914 2.914 55.876 9 5.819 2.819 4.249 2.249 38.874 10 5.984 2.984 5.147 3.147 68.497 20 15 2 5.147 2.147 4.271 2.271 24.984 18 5.078 2.078 4.014 2.014 14.872 20 5.618 2.618 5.081 3.081 69.187 40 30 3 5.491 2.491 4.941 2.941 57.078 38 5.107 2.107 4.028 2.028 23.174 30 5.347 2.347 4.627 2.627 70.842 60 45 3 5.148 2.148 4.489 2.489 58.247 58 5.004 2.004 4.309 2.309 41.872 40 5.334 2.334 4.658 2.658 74.194 80 65 5 5.238 2.238 4.748 2.748 60.827 78 4.997 1.997 4.102 2.102 47.145 50 0.447 0.553 1.39 0.19 1.987 100 75 5 0.474 0.526 1.317 0.117 1.854 98 1.218 0.218 1.234 0.034 1.823
(d)
MLE Standard deviation MLE Standard deviation 5 1.395 0.395 2.717 0.717 42.175 10 7 2 1.501 0.501 2.585 0.585 35.214 9 1.014 0.014 2.461 0.461 18.258 10 1.284 0.284 2.648 0.648 40.954 20 15 2 1.481 0.481 2.441 0.441 33.254 18 1.008 0.008 2.314 0.314 16.418 20 1.658 0.658 2.995 0.995 68.284 40 30 3 1.018 0.018 2.147 0.147 50.258 38 1.001 0.001 1.654 0.346 52.547 30 1.228 0.228 2.954 0.954 68.952 60 45 3 1.109 0.109 2.756 0.756 53.218 58 1.019 0.019 2.341 0.341 40.021 40 1.721 0.721 2.481 0.481 77.248 80 65 5 1.856 0.856 2.441 0.441 80.514 78 1.007 0.007 1.761 0.239 54.951 50 1.395 0.395 2.717 0.717 42.175 100 75 5 1.501 0.501 2.585 0.585 35.214 98 1.014 0.014 2.461 0.461 18.258