Uncertainty measurement and expression can be considered in different ways, but by using coverage interval is the most popular method if considering the bounding information. In this paper, we derive the theoretical probability distribution function of coverage interval and verify that its accuracy meets the best of fit. We illustrate that it may help the decision of the curve shape for the general expanded uncertainty task. We also suggest a new algorithm for the purpose of connecting the coverage interval to the statistical coverage interval which is robust on the confidence level representation for sparse data. In final, we extend the statistical coverage interval to a new more accurate representation of probability propagation of coverage interval. Experiments showed this new approach was robust especial in the sparse data condition.