On Inverse Moments Of Two Nonnegative Dependent Sequences

In recent years the inverse moment widely used in various fields, They may beapplied in powers of tests, evaluating risks of estimations,post-stratification, lifetesting, reliability analysis, complex systems, insurance and financial mathematics,and others. The asymptotic approximation of inverse moments of the normalizedsums of the nonnegative NOD random variables is obtained under the finite firstmoments condition. In particular, the asymptotic approximation of inverse momentsholds true for the partial sums. The main result extends Wang Xuejun’s results fromthree aspects. It’s said that change the finite second moments to the finite firstmoments, make the regular factors have nothing with the sum of variance. We notonly study the inverse of regular summation but also study the inverse of the part ofthe regular summation. And we proof the results with Rosenthal’s type inequalityinstead of exponent inequality. Then extend the new results of the inverse moments ofnonnegative NOD Sequence to nonnegative ρ~Sequence.