An Optimization-Based Approach to Calculate Confidence Interval on Mean Value with Interval Data

Table 1

Methods for calculating moment bounds for multiple interval data.

Moment	Formula
1	𝑀𝑀=1𝑛^𝑛∑𝑖𝑙𝑏𝑖,1𝑛^𝑛∑𝑖𝑢𝑏𝑖
2	min/max𝑥1,…,𝑥𝑛𝑀2=1𝑛^𝑛𝑖∑=1𝑥𝑖−1𝑛^𝑛𝑗∑=1𝑥𝑗^2s.t.𝑙𝑏𝑖≤𝑥𝑖≤𝑢𝑏𝑖𝑖={1,…,𝑛}
3	min/max𝑥1,…,𝑥𝑛𝑀3=1𝑛^𝑛𝑖∑=1𝑥𝑖−1𝑛^𝑛𝑗∑=1𝑥𝑗^3s.t.𝑙𝑏𝑖≤𝑥𝑖≤𝑢𝑏𝑖𝑖={1,…,𝑛}

Note: 𝑙𝑏_𝑖𝑢𝑏_𝑖: set of intervals; 𝑛: number of intervals.