A unified method for constructing expectation tolerance intervals

摘要

Given a random sample of size n with mean X and standard deviation s from a symmetric distribution F(x; μ, σ) = F_0((x - μ)/σ) with F0 known, and X ~ F(x; μ, σ) independent of the sample, we show how to construct an expansion a'_n = ∑_(i=0)~∞ c_i n~(-i) such that X - sa'_n < X < X + sa'_n with a given probability β. The practical value of this result is illustrated by simulation and using a real data set.