Complete Moment Convergence And Integral Convergence Of END Random Variable Sequences

Extended negatively dependent(END)random variables are a broader class of dependent ran-dom variables,which includes independent random variable,negatively associated(NA)ran-dom variable,negatively orthant dependent(NOD)random variable.It is of great significance to study the application of extended negatively dependent random variables in actuarial insur-ance,big data statistics and other fields.In this thesis,by using the basic properties of END random variable sequence,Rosenthal type moment inequality,Jensen inequality,Markov inequality,C_rinequality,other important inequalities and the properties of slowly varying function,and then take appropriate trunca-tion technology,the complete moment convergence and the equivalent conditions of complete moment convergence and complete integral convergence are obtained.In Chapter 2.Firstly,the complete moment convergence and integral convergence of the END random variable sequence is obtained by combining the properties of slowly varying function and some conclusions are obtained.Secondly,the equivalent conditions of complete momen-t convergence and integral convergence of the END random variable sequence are obtained when the slowly varying function is monotonically increasing,and the corresponding conclu-sions are improved when r=1,the existing results are extended.In Chapter 3,the complete moment convergence of END random variable sequence with de Bruijn conjugate function is studied,an sufficient condition for complete moment convergence is obtained.