Linear Regression Estimation Methods for Inferring Standard Values of Snow Load in Small Sample Situations

Abstract

The aim of this paper is to establish a new method for inferring standard values of snow load in small sample situations. Due to the incomplete meteorological data in some areas, it is often necessary to infer the standard values of snow load in the conditions of small samples in engineering, but the point estimation methods of classical statistics adopted till now do not take into account the influences of statistical uncertainty, and the inference results are always aggressive. In order to overcome the above shortcomings, according to the basic principle of optimal linear unbiased estimation and invariant estimation of the minimum type I distribution parameters and the tantile, using the least square method, the linear regression estimation methods for inferring standard values of snow load in small sample situations are proposed, which can take into account two cases such as parameter-free and known coefficient of variation, and the predicted formulas of snow load standard values are given, respectively. Through numerical integration and Monte Carlo numerical simulation, the numerical table of correlation coefficients is established, which is more convenient for the direct application of inferential formulas. According to the results of theoretical analysis and examples, when using the indirect point estimation methods to infer the standard values of snow load in the conditions of small samples, the inference results are always small. The linear regression estimation method is suitable for inferring standard values of snow load in the conditions of small samples, which can give more reasonable results. When using the linear regression estimation to infer standard values of snow load in practical application, even if the coefficient of variation is unknown, it can set the upper limit value of the coefficient of variation according to the experience; meanwhile, according to the parameter-free and known coefficient of variation, the estimation is carried out, respectively, and the smaller value of the two is taken as the final estimate. The method can be extended to the statistical inference of variable load standard values such as wind load and floor load.