An improved method for estimating bootstrap confidence interval of quantile function

This paper presents an improved method for estimating the bootstrap confidence interval of the quantile function, aimed at precisely assessing the distribution of product performance. The method begins by refining the quantile function estimation technique, integrating maximum entropy with fractional probability weighted moments, and developing a single-loop optimization method that is both efficient and robust for determining distribution parameters. This approach is then augmente d with an improved bootstrap sampling method to estimate the confidence interval of the quantile function. The proposed methodology capitalizes on the strengths of combining probability-weighted moments with maximum entropy and the bootstrap technique. It is characterized by its distribution type independence and not sensitive to outliers samples. Moreover, it effectively determines the confidence interval of the quantile function, even from very small samples. The superiority of thi s method is comprehensively validated through various test cases.