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ON THE ALMOST SURE CONVERGENCE OF WEIGHTED SUMS OF NA RANDOM VARIABLES

Kim, T.S.    (Department of Statistics and Institute of Basic Natural Science, Wonkwang University   ); Ko, M.H.    (Department of Statistics and Institute of Basic Natural Science, Wonkwang University   ); Lee, Y.M.    (Department of Statistics and Institute of Basic Natural Science, Wonkwang University   ); Lin, Z.    (Department of Mathematics, Zhejiang University  );
  • 초록

    Let {X, $X_{n}, n\;{\geq}\;1$ } be a sequence of identically distributed, negatively associated (NA) random variables and assume that $│X│^{r}$ , r > 0, has a finite moment generating function. A strong law of large numbers is established for weighted sums of these variables.


  • 주제어

    Negatively associated random variables .   strong law of large numbers .   identically distributed .   moment generating function .   weighted sum.  

  • 참고문헌 (13)

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    4. Stout,W.F. , Almost Sure Convergence / v.,pp.,
    5. A comparison theorem on moment inequalities between negatively associated and independent random variables , Shao,Q.M. , Journal of Theoretical Probability / v.13,pp.343-356,
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    7. Asymptotic independence and limit theorems for positively and negatively dependent random variables , Newman,C.M. , IMS Lecture Notes Monograph Series. Vol. 5. / v.,pp.,
    8. Limiting behavior of weighted sums of independent random variables , Chow,Y.S.;Lai,T.L. , The Annals of Probability / v.1,pp.810-824,
    9. Almost certain convergence in double arrays , Teicher,H. , Zeitschrift fur wahrscheinlichkeitstheorie und Verwandte Gebiets / v.69,pp.331-345,
    10. Almost sure convergence of weighted sums of XA sequences , Cheng,R.;Gan,S. , Wuhan University Journal of Natural Sciences / v.3,pp.11-16,
    11. Negative association of random variables with applications , Joag Dev,K;Proschan,F. , The Annals of Statistics / v.11,pp.286-295,
    12. A note on the almost sure convergence of sums of negatively dependent random variables , Matula,P. , Statistics & Probability Letters / v.15,pp.209-213,
    13. Marcinkiewicz strong laws for linear statistics , Bai,Z.D.;Cheng,P.E. , Statistics & Probability Letters / v.46,pp.105-112,

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