Statistical Diagnosis Of Logarithmic Generalized Inverse Weibull Distribution Regression Model

The generalized inverse Weibull distribution(GIW)is a three-parameter life distribution extended on the basis of the inverse Weibull distribution.Due to its applicability and flexibility in describing product life,the generalized inverse Weibull distribution is widely used in biology.In the fields of medicine,engineering,etc.It is well known that,for example,life is often affected by many factors.In order to establish the correlation between life data and these covariates,a regression model is constructed to establish statistical relationships and to analyze and analyze by regression analysis.The logarithmic linear relationship between variables is often presented.In the second chapter,we logarithmize the generalized inverse Weibull distribution and establish a logarithmic generalized inverse Weibull distribution(LGIW)regression model,and estimate the parameters of the model.The traditional maximum likelihood estimation based on Newton-Gaussian iteration is over-dependent on the initial value(the choice of initial value affects the convergence degree and even convergence),so the Newton-Gaussian iteration is modified to obtain the maximum iterative stability.Likelihood estimation,and numerical simulation to explore the simulation effect of parameter estimation.Simulation shows that iteratively corrected the maximum likelihood estimation effect is significant,and as the sample size increases,the number of iterations decreases,and the parameter estimates are closer to the true value.As one of the most widely used and most important models in statistical diagnosis methods,the data deletion model has been widely applied to the statistical diagnosis of various regression models.The third chapter is based on the LGIW regression model to establish the data deletion model of the model.And obtain the parameter estimation of the data deletion model and its onestep approximation.In addition,based on the data deletion model,the corresponding diagnostic statistic and its one-step approximation(Cook distance,likelihood distance and WK statistic)are obtained.Finally,the numerical simulation and case analysis are passed.These diagnostic statistics intuitively detect strong influence points or abnormal points,and can accurately detect artificial abnormal points,which proves the validity of the model and its diagnostic statistics.In the fourth chapter,the hypothesis test of regression coefficients of LGIW regression model is studied.The regression coefficient of regression model is tested by the existence test and the homogeneity test based on parameterization.The corresponding score test statistic is obtained,and the second pass value is obtained.Simulation and case analysis illustrate the effectiveness of the methods and Score test statistics in this chapter.