Research Article

On the Order Statistics of Standard Normal-Based Power Method Distributions

Table 3

Expected values of order statistics for 𝑝 1 ( 𝑍 ) = 𝑍 for 𝑛 = 4 , 5 .

𝐸 [ 𝑝 1 ( 𝑍 ) 3 4 3 ] = 𝜋 + 1 8 t a n 1 ( 1 / 2 ) 𝜋 3 / 2 = 0 . 2 9 7 0 1 1 3 8
𝐸 [ 𝑝 1 ( 𝑍 ) 4 4 3 ] = 𝜋 6 t a n 1 ( 1 / 2 ) 𝜋 3 / 2 = 1 . 0 2 9 3 7 5 3 7
𝐸 [ 𝑝 1 ( 𝑍 ) 3 5 ] = 0
𝐸 [ 𝑝 1 ( 𝑍 ) 4 5 5 ] = 𝜋 + 3 0 t a n 1 ( 1 / 2 ) 𝜋 3 / 2 = 0 . 4 9 5 0 1 8 9 7
𝐸 [ 𝑝 1 ( 𝑍 ) 5 5 5 ] = 𝜋 1 5 t a n 1 ( 1 / 2 ) 𝜋 3 / 2 = 1 . 1 6 2 9 6 4 4 7