Research Article

Bayesian Inference on the Shape Parameter and Future Observation of Exponentiated Family of Distributions

Table 2

HPD intervals of the shape parameter for the data set.

𝑐 1 ( 𝐻 𝐸 1 , 𝐻 𝐸 2 )
𝜂 = 0 . 0 1 𝜂 = 0 . 0 5 𝜂 = 0 . 1 0

0.5 ( 2 . 6 3 1 , 7 . 9 9 7 ) ( 2 . 9 9 9 , 7 . 0 7 9 ) ( 3 . 0 1 9 , 6 . 5 3 1 )
1.0 ( 2 . 4 7 2 , 7 . 7 1 8 ) ( 2 . 9 0 2 , 6 . 8 7 8 ) ( 2 . 9 9 9 , 6 . 3 6 1 )
1.5 ( 2 . 3 1 4 , 7 . 4 3 7 ) ( 2 . 7 2 9 , 6 . 6 1 2 ) ( 2 . 9 6 1 , 6 . 2 1 4 )
2.0 ( 2 . 1 5 8 , 7 . 1 5 4 ) ( 2 . 5 5 8 , 6 . 3 4 4 ) ( 2 . 7 8 2 , 5 . 9 5 4 )
5.0 ( 2 . 0 6 1 , 7 . 0 5 2 ) ( 2 . 3 6 5 , 6 . 1 3 1 ) ( 2 . 5 3 2 , 5 . 6 9 1 )
( 𝐻 𝑐 1 , 𝐻 𝑐 2 ) ( 2 . 1 0 8 , 7 . 0 6 5 ) ( 2 . 2 3 6 , 6 . 4 5 2 ) ( 2 . 8 7 1 , 6 . 1 4 1 )