On multivariate compound distributions

Theory of Probability and its Applications

Volumn 47, Issue 3, 2003, Pages 493-505

  Cekanavicius V ^a  

^a VILNIUS UNIVERSITY   (Lithuania)

Author keywords

Compound poisson distribution; The first uniform kolmogorov theorem; Total variation

Indexed keywords

EID: 0141429918     PISSN: 0040585X     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (19)

1. A. K. ALEŠKEVIČIENÉ AND V. A. STATULEVIČIUS, Large deviations in power zones in approximation by the Poisson law, Russian Math. Surveys, 50 (1995), pp. 905-924.
2. T. V. ARAK AND A. Yu. ZAǏTSEV, Uniform Limit Theorems for Sums of Independent Random Variables, Proceedings of the Steklov Institute of Mathematics 1, AMS, Providence, RI, 1988.
3. V. BENTKUS, F. GÖTZE, AND A. Yu. ZAITSEV, Approximation of quadratic forms of independent random vectors by accompanying laws, Theory Probab. Appl., 42 (1997), pp. 189-212.
4. A. BIKYALIS AND A. ŽEMAITIS, Asymptotic expansions for large deviations probabilities, Primen. Teor. Veroyatnost. i Mat. Statist., 3 (1980), pp. 9-39 (in Russian).
5. K. A. BOROVKOV AND D. PFEIFER, On improvements of the order of approximation in the Poisson limit theorem, J. Appl. Probab., 33 (1996), pp. 146-155.
6. V. ČEKANAVIČIUS, On asymptotic expansions in the first uniform Kolmogorov theorem, Statist. Probab. Lett., 25 (1995), pp. 145-151.
7. V. ČEKANAVIČIUS, On compound approximations, Probab. Math. Statist., 16 (1996), pp. 275-285.
8. V. ČEKANAVIČIUS, Estimates in total variation for convolutions of compound distributions, J. London Math. Soc., 58 (1998), pp. 748-760.
9. A. N. KOLMOGOROV, Two uniform limit theorems for sums of independent random variables, Theory Probab. Appl., 1 (1956), pp. 384-394.
10. A. N. KOLMOGOROV, On the approximation of distributions of sums of independent summands by infinitely divisible distributions, Sankhyā Ser. A, 25 (1963), pp. 159-174.
11. L. LE CAM, On the distribution of sums of independent random variables, in Bernoulli 1713, Bayes 1763, Laplace 1813. Anniversary Volume, J. Neyman and L. Le Cam, eds., SpringerVerlag, Berlin, Heidelberg, 1965, pp. 179-202.
12. E. L. PRESMAN, On a multidimensional version of the Kolmogorov uniform limit theorem, Theory Probab. Appl., 18 (1973), pp. 378-384.
13. E. L. PRESMAN, Approximation of binomial distributions by infinitely divisible ones, Theory Probab. Appl., 28 (1983), pp. 393-403.
14. Yu. V. PROKHOROV, On sums of identically distributed random variables, Dokl. Akad. Nauk SSSR, 105 (1955), pp. 645-647 (in Russian).
15. Yu. V. PROKHOROV, On a uniform limit theorem of A. N. Kolmogorov, Theory Probab. Appl., 5 (1960), pp. 98-106.
16. V. V. SAZONOV, On the closeness of distributions of sums of independent random variables and the class of infinitely divisible distributions in the multidimensional case, Trudy Tbilis. Univ., A4 (146) (1972), pp. 29-37 (in Russian).
17. J. ŠIAULYS AND V. ČEKANAVIČIUS, Approximation of distributions of integer-valued additive functions by discrete charges. I, Lithuanian Math. J., 28 (1988), pp. 392-401.
18. Y. H. WANG, On the multivariate compound distributions, J. Multivariate Anal., 59 (1996), pp. 13-21.
19. A. Yu. ZAITSEV, On the approximation of convolutions of multidimensional symmetric distributions by accompanying laws, J. Soviet. Math., 61 (1992), pp. 1859-1872.