Asymptotic expansion for the density function of the series scheme of a random variables in the large deviation in Cramer zone
In this work, the expansion of the density function of series schemes of independent variables ξ(n)1,ξ(n)2 ,..., ξ(n)j, with means Eξ(n)j = 0, and dispersions σ(n)2j = Eξ(n)2j has been obtained in the Cramer zone of large deviations. The result was obtained, based on General Lemma 6.1 [2] by jo...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Vilnius University Press
2001-12-01
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| Series: | Lietuvos Matematikos Rinkinys |
| Online Access: | https://www.zurnalai.vu.lt/LMR/article/view/34742 |
| Summary: | In this work, the expansion of the density function of series schemes of independent variables ξ(n)1,ξ(n)2 ,..., ξ(n)j, with means Eξ(n)j = 0, and dispersions σ(n)2j = Eξ(n)2j has been obtained in the Cramer zone of large deviations. The result was obtained, based on General Lemma 6.1 [2] by joining the methods of characteristic functions and cumulants. The work broadens theory of sums of random variables [1] and in special case improves S.A. Book [5] results of sums of random variables with weights.
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| ISSN: | 0132-2818 2335-898X |