分析常用7种统计分布的统一线性回归方法

UNIFIED LINEAR REGRESSION METHOD FOR THE ANALYSIS OF SEVEN COMMONLY USED STATISTICAL DISTRIBUTIONS

发展了分析 7种常用假设分布即三参数Weibull、两参数Weibull、正态、对数正态、极小值、极大值和指数分布的统一线性回归方法。方法中 7种常用分布的统计参量及其置信限 ,以及概率的置信限 ,都采用线性回归方法完成。统计检验采用Pearson统计参量———线性相关系数r来方便进行。满足假设分布的临界r值采用r—t分布函数变换得到。方法为从 7种常用分布中确定良好假设分布奠定了基础。经工程材料

A unified linear regression method for the analysis of seven commonly used statistical distributions, namely Weibull (two-and three-parameter), normal, lognormal, extreme minimum value, extreme maximum value, and exponential, is developed. In the method, statistical parameters and their confidence bounds, and probability confidence bounds of the seven distributions are evaluated by a linear regression method. Statistical tests of the distributions are conveniently made by the Pearson statistical parameter-linear relationship coefficient r. Critical value of the r for an accepted distribution is determined by a transformation of r-to-t-distribution function This method provides a basis of determining an appropriate assumed distribution from the seven distributions in analysis of random data. Availability of this method has been verified by an analysis of the cyclic stress amplitude data of a engineering material, 1Cr18Ni9Ti stainless steel pipe-weld metal, and previous analyses of the fatigue life and crack growth rate data of engineering materials.