Research Article
Bayesian Estimation of Inequality and Poverty Indices in Case of Pareto Distribution Using Different Priors under LINEX Loss Function
Table 5
Estimated loss functions for
α, G, M, and
using different priors under the assumptions of SELF.
| | | |
Uniform prior |
Jeffrey’s prior | Conjugate prior | = 0.5 = 2 | = 2 = 2 |
| For | 40 | 2.5 | 0.198417 | 0.188773 | 0.105229 | 0.149043 | 3.5 | 0.545553 | 0.315654 | 0.301779 | 0.303094 | 4.5 | 0.636095 | 0.546807 | 0.511984 | 0.662855 | 100 | 2.5 | 0.081056 | 0.080694 | 0.065290 | 0.072233 | 3.5 | 0.178339 | 0.192881 | 0.138684 | 0.139510 | 4.5 | 0.261753 | 0.299142 | 0.231038 | 0.215135 |
| For | 40 | 2.5 | 0.002541 | 0.002135 | 0.001879 | 0.053437 | 3.5 | 0.001215 | 0.001071 | 0.001055 | 0.033683 | 4.5 | 0.000989 | 0.000629 | 0.000222 | 0.026677 | 100 | 2.5 | 0.001347 | 0.001311 | 0.001054 | 0.011318 | 3.5 | 0.000604 | 0.000408 | 0.000407 | 0.006967 | 4.5 | 0.000228 | 0.000236 | 0.000165 | 0.005405 |
| For | 40 | 2.5 | 0.085215 | 0.075152 | 0.061571 | 0.097215 | 3.5 | 0.092519 | 0.085051 | 0.070570 | 0.102310 | 4.5 | 0.157210 | 0.115720 | 0.095721 | 0.105721 | 100 | 2.5 | 0.105721 | 0.097121 | 0.050712 | 0.098721 | 3.5 | 0.097215 | 0.070125 | 0.033710 | 0.059713 | 4.5 | 0.080712 | 0.052325 | 0.092530 | 0.082173 |
| For | 40 | 2.5 | 0.003513 | 0.004420 | 0.003916 | 0.005192 | 3.5 | 0.001382 | 0.003596 | 0.002156 | 0.004921 | 4.5 | 0.001224 | 0.001993 | 0.001057 | 0.003051 | 100 | 2.5 | 0.001152 | 0.001907 | 0.001805 | 0.001982 | 3.5 | 0.000538 | 0.000914 | 0.000705 | 0.001572 | 4.5 | 0.000260 | 0.000896 | 0.000679 | 0.000971 |
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