International Scholarly Research Notices

Research Article

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

Table 2

Computed values of the remainder term 𝜀 𝑘 associated with (2.23). The values were computed with 40-digit precision.
Sample size ( 𝑛 )IntegralRemainder term
1 , … , 5 𝐼 1 , 𝐼 3 𝜀 1 = 0 . 0
6 , 7 𝐼 5 𝜀 2 = 0 . 0 3 1 4 0 6 9 8 8 2 9 5 5 2 0 1 0 2 7 0 7 3 1 9 3 7 9 5 0 8 8 1 2 7 6 5 0 0 5 9 5
8 , 9 𝐼 7 𝜀 3 = 0 . 0 5 1 5 6 0 6 8 6 5 0 0 3 1 4 0 9 7 8 7 1 7 0 3 9 2 9 1 9 3 1 2 6 5 6 8 5 8 2 4 6
1 0 , 1 1 𝐼 9 𝜀 4 = 0 . 0 5 9 0 0 1 9 8 7 1 0 3 5 5 8 1 7 1 4 9 8 6 8 4 2 3 8 1 7 9 2 8 4 6 5 2 1 2 2 9 8
1 2 , 1 3 𝐼 1 1 𝜀 5 = 0 . 0 5 8 0 8 9 7 5 4 5 8 2 0 3 6 3 8 9 6 8 8 8 2 5 2 2 5 9 3 4 1 3 6 6 0 3 7 1 3 4 8
1 4 , 1 5 𝐼 1 3 𝜀 6 = 0 . 0 5 2 7 4 7 6 3 6 1 6 7 6 1 4 2 2 2 2 1 7 0 9 6 2 6 5 2 3 9 3 5 9 9 8 4 6 3 5 3 9
1 6 , 1 7 𝐼 1 5 𝜀 7 = 0 . 0 4 5 5 9 2 3 6 5 7 4 1 0 4 6 4 3 5 3 0 7 4 8 5 9 3 7 5 8 5 4 4 7 4 5 9 4 9 6 7 6
1 8 , 1 9 𝐼 1 7 𝜀 8 = 0 . 0 3 8 1 5 2 2 3 8 9 5 2 3 4 4 5 3 7 7 9 2 7 4 1 2 7 8 6 1 5 7 2 4 2 3 8 8 7 8 7 7
2 0 , 2 1 𝐼 1 9 𝜀 9 = 0 . 0 3 1 2 2 2 0 5 6 9 1 4 6 7 1 6 8 4 8 9 7 1 8 5 5 6 8 7 0 6 8 2 2 7 0 6 3 6 0 5 5
2 2 , 2 3 𝐼 2 1 𝜀 1 0 = 0 . 0 2 5 1 4 8 5 5 2 5 4 6 1 4 8 6 5 6 7 0 2 0 9 1 2 2 2 8 8 5 9 6 2 4 1 8 0 3 0 4 7
2 4 , 2 5 𝐼 2 3 𝜀 1 1 = 0 . 0 2 0 0 2 4 2 9 9 2 1 4 0 5 3 5 4 5 6 0 4 0 5 5 8 8 0 7 5 4 3 8 6 6 6 4 6 0 5 7 0
2 6 , 2 7 𝐼 2 5 𝜀 1 2 = 0 . 0 1 5 8 0 9 2 8 6 8 1 2 6 3 6 3 2 3 9 8 7 5 3 7 0 7 6 8 5 2 3 2 8 7 9 7 2 3 1 5 4
⋮ ⋮ ⋮
5 2 , 5 3 𝐼 5 1 𝜀 2 5 = 0 . 0 0 0 5 7 4 5 5 5 9 7 4 5 3 3 3 2 8 0 5 0 7 3 4 0 9 0 7 4 4 8 7 2 3 6 5 8 4 2 3 2
⋮ ⋮ ⋮
1 0 2 , 1 0 3 𝐼 1 0 1 𝜀 5 0 = 0 . 0 0 0 0 0 0 9 9 1 9 3 6 1 4 7 6 9 4 6 1 0 6 5 7 4 5 2 5 2 6 1 6 9 8 7 0 8 2 8 5 9