Considerations on a new approach of the confidence interval for population mean

In statistical analysis the usefulness of confidence intervals is undeniable. Taking into account the uncertainty associated with samples, the estimation of the population parameters can be performed by confidence intervals. In other words, as long as there is randomness and finite sample size (which define the reality) estimation of statistical indicators will be done by confidence intervals. Inspired by the methods used for proportions (frequency of an event), we propose and study a new confidence interval for the mean of a continuous random variable. The main idea comes from the Wilson interval and we shape a similar formula for computing the mean bounds. Numerical simulation results show advantages but also limitations of the newly proposed method.