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...
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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 |
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| author | Dovilė Deltuvienė Leonas Saulis |
| author_facet | Dovilė Deltuvienė Leonas Saulis |
| author_sort | Dovilė Deltuvienė |
| collection | DOAJ |
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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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| format | Article |
| id | doaj-art-f23c7882d5444b0db84e9d9c9b201aee |
| institution | Kabale University |
| issn | 0132-2818 2335-898X |
| language | English |
| publishDate | 2001-12-01 |
| publisher | Vilnius University Press |
| record_format | Article |
| series | Lietuvos Matematikos Rinkinys |
| spelling | doaj-art-f23c7882d5444b0db84e9d9c9b201aee2025-02-11T18:14:04ZengVilnius University PressLietuvos Matematikos Rinkinys0132-28182335-898X2001-12-0141spec.10.15388/LMR.2001.34742Asymptotic expansion for the density function of the series scheme of a random variables in the large deviation in Cramer zoneDovilė Deltuvienė0Leonas Saulis1Vilnius Gediminas Technical UniversityVilnius Gediminas Technical University 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. https://www.zurnalai.vu.lt/LMR/article/view/34742 |
| spellingShingle | Dovilė Deltuvienė Leonas Saulis Asymptotic expansion for the density function of the series scheme of a random variables in the large deviation in Cramer zone Lietuvos Matematikos Rinkinys |
| title | Asymptotic expansion for the density function of the series scheme of a random variables in the large deviation in Cramer zone |
| title_full | Asymptotic expansion for the density function of the series scheme of a random variables in the large deviation in Cramer zone |
| title_fullStr | Asymptotic expansion for the density function of the series scheme of a random variables in the large deviation in Cramer zone |
| title_full_unstemmed | Asymptotic expansion for the density function of the series scheme of a random variables in the large deviation in Cramer zone |
| title_short | Asymptotic expansion for the density function of the series scheme of a random variables in the large deviation in Cramer zone |
| title_sort | asymptotic expansion for the density function of the series scheme of a random variables in the large deviation in cramer zone |
| url | https://www.zurnalai.vu.lt/LMR/article/view/34742 |
| work_keys_str_mv | AT doviledeltuviene asymptoticexpansionforthedensityfunctionoftheseriesschemeofarandomvariablesinthelargedeviationincramerzone AT leonassaulis asymptoticexpansionforthedensityfunctionoftheseriesschemeofarandomvariablesinthelargedeviationincramerzone |