Approximate Calculation Method for Noncentral t-Distribution Quantile

Abstract

In the process of structural design and structural performance evaluation, the inference of the reliable life of the structure and the representative value of the material strength is a necessary work. The determination of material strength is the presumption of the quantile of the normal distribution, and the determination of the confidence level of the quantile of the normal distribution involves the noncentral t-distribution function. However, the calculation of the quantile is very complicated and is often provided in the form of a numerical table, which often involves multiparameter interpolation calculation, so it is not convenient to apply. The existing approximate calculation methods for noncentral t-distribution quantiles have strict application conditions, and the calculation process is relatively cumbersome. It is still difficult to meet actual needs in terms of fitting accuracy, application range, and convenience. In this paper, a new calculation method for noncentral t-distribution quantiles is proposed by introducing new probability expressions and related approximate distributions, based on theoretical derivation and numerical fitting. The comparative analysis results show that the method not only is convenient for calculation but also has the advantages of higher accuracy and wider application range, and it is more in line with the actual needs of engineering.