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Journal of Probability and Statistics
/
2011
/
Article
/
Tab 4
/
Research Article
Bayesian Inference on the Shape Parameter and Future Observation of Exponentiated Family of Distributions
Table 4
Bayesian predictive and HPD predictive intervals for future observation of the data set.
𝜂
Conjugate prior
𝑐
1
=
0
.
5
𝑐
1
=
1
.
0
𝑐
1
=
1
.
5
𝑐
1
=
2
.
0
𝑐
1
=
5
.
0
0.01
(0.015, 17.32)
(
0
.
0
3
1
,
3
7
.
6
1
)
(
0
.
0
3
3
,
3
9
.
5
3
)
(
0
.
0
3
4
,
4
1
.
6
6
)
(
0
.
0
3
6
,
4
4
.
0
3
)
(
0
.
0
5
1
,
6
6
.
7
8
)
(7.819, 220.83)
(
5
.
9
6
6
,
1
9
9
.
8
2
)
(
5
.
2
5
7
,
1
9
8
.
2
9
)
(
4
.
5
5
2
,
1
9
6
.
6
7
)
(
3
.
8
5
6
,
1
9
4
.
9
7
)
(
0
.
3
9
8
,
1
8
2
.
5
3
)
0.05
(0.078, 11.85)
(
0
.
1
5
9
,
2
5
.
2
5
)
(
0
.
1
6
7
,
2
6
.
4
9
)
(
0
.
1
7
5
,
2
7
.
8
7
)
(
0
.
1
8
3
,
2
9
.
4
1
)
(
0
.
2
6
2
,
4
3
.
7
6
)
(16.206, 168.96)
(
1
0
.
7
1
2
,
1
4
8
.
2
6
)
(
1
0
.
2
1
7
,
1
4
7
.
4
5
)
(
9
.
6
5
4
,
1
4
6
.
4
1
)
(
8
.
6
7
1
,
1
4
4
.
6
9
)
(
2
.
6
3
5
,
1
3
1
.
9
0
)
0.10
(0.158, 9.55)
(
0
.
3
2
4
,
2
0
.
1
9
)
(
0
.
3
3
8
,
2
1
.
1
7
)
(
0
.
3
5
4
,
2
2
.
2
5
)
(
0
.
3
7
2
,
2
3
.
4
5
)
(
0
.
5
3
2
,
3
4
.
6
3
)
(26.138, 146.11)
(
1
4
.
1
7
6
,
1
2
4
.
4
8
)
(
1
3
.
8
1
2
,
1
2
3
.
3
7
)
(
1
2
.
1
0
3
,
1
2
2
.
2
8
)
(
1
0
.
9
1
6
,
1
2
1
.
2
4
)
(
4
.
9
3
9
,
1
1
0
.
2
2
)
