Small Sample Method And Applied Technology For Determining Confidence Limit Of Normal Population Percentile

Small sample method is used to improve the forecast accuracy when the amount of in-site test data is less. The method combines the personalized information of few in-site data and the general information of previous experiential data. Then, the integral information required to predict is coming, which increases the forecast accuracy.Based on the issue of small sample method, four groups of formulas of normal population percentile confidence limit and the confidence interval are provided in this paper. The four groups of formulas make full use of the personalized information of smaller in-site samples and the general information of others, then significantly shorten the value of percentile confidence interval length and improve the forecast accuracy. Meanwhile, these are effective ways to avoid the present sample information being inundated by others. On the other hand, these formulas present the confidence interval and the confidence limit of very small sample, which would make the test results having higher practice value.In order to verify the effectiveness of the four groups of formulas, Monte Carlo method is used to simulate the present data and history test data. And the massive examinations show that these formulas in the paper can greatly reduce the confidence interval length. At same time, the lower and upper confidence limit fit the actual population percentile better than using traditional formulas in the same confidence.These formulas in the paper are applied to practice such as determining fatigue limits of metallic material and the concrete strength which effectively improves the accuracy of the test results, thus greatly reduces the uncertainties of the assessment outcome.In engineering practice, many mathematical meanings of the physics are relative to the normal population percentile, thus these formulas given in this paper can be used to solve similar problems in other areas.