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

Xudong Wang,Jitao Yao

doi:10.1155/2020/3753417

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.

Highlights

Snow load is one of the main loads of buildings, and the inference of its standard value is the basis for the establishment of structural design and evaluation methods
A method for estimating the maximum type I distribution parameters and tantile is proposed in the paper [21], which lays a theoretical foundation for the small sample inference of the standard values of snow load without parameter information. erefore, the inference formula of the standard values of snow load without parameter information can be established
Based on the above analysis, the probability distribution model of snow load is established first in this paper because the standard values of snow load usually are expressed as a tantile of the distribution, type I maximum distribution, and type I minimum distribution which belong to the same extreme value distribution families and can be converted with each other; by using the least square method based on the best linear unbiased estimation and the invariant estimation principle of the current minimum type I distribution parameters, a linear regression estimation method for standard snow load under small sample conditions is proposed [22,23,24,25,26,27,28,29,30,31]

Summary

Introduction

Snow load is one of the main loads of buildings, and the inference of its standard value is the basis for the establishment of structural design and evaluation methods. A method for estimating the maximum type I distribution parameters and tantile is proposed in the paper [21], which lays a theoretical foundation for the small sample inference of the standard values of snow load without parameter information. Based on the above analysis, the probability distribution model of snow load is established first in this paper because the standard values of snow load usually are expressed as a tantile of the distribution, type I maximum distribution, and type I minimum distribution which belong to the same extreme value distribution families and can be converted with each other; by using the least square method based on the best linear unbiased estimation and the invariant estimation principle of the current minimum type I distribution parameters, a linear regression estimation method for standard snow load under small sample conditions is proposed [22,23,24,25,26,27,28,29,30,31]. E inference formula of standard values of snow load is given in this paper, and no parameter information and the known coefficient of variation are both considered. rough numerical integration and Monte Carlo numerical simulation, a numerical table of correlation coefficient is established to tantile the application of the inference formula, and the conclusions and suggestions are given by comparing the results with the traditional large sample method. e method can be extended to the statistical inference of variable load standard values such as wind load and floor load

Probability Distribution Model of Snow Load

Linear Regression Estimation Method for Standard Values of Snow Load

Linear Unbiased Estimation of Distribution

Examples

Conclusions