On stability estimations without any conditions of symmetry
Let X, X1, X2, ..., Xn be i.i.d. random variables. B. Ramachandran and C.R. Rao have proved that if distributions of sample mean ‾X = ‾X(n) = (X1 + ⋯ + Xn)/n and monomial X are coincident at least at two points n = j1 and n = j2 such that log j1/ log j2 is irrational, then X follows a Cauchy law. A...
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Vilnius University Press
2023-09-01
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| Series: | Lietuvos Matematikos Rinkinys |
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| Online Access: | https://www.zurnalai.vu.lt/LMR/article/view/30793 |
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| author | Romanas Januškevičius Olga Januškevičienė |
| author_facet | Romanas Januškevičius Olga Januškevičienė |
| author_sort | Romanas Januškevičius |
| collection | DOAJ |
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Let X, X1, X2, ..., Xn be i.i.d. random variables. B. Ramachandran and C.R. Rao have proved that if distributions of sample mean ‾X = ‾X(n) = (X1 + ⋯ + Xn)/n and monomial X are coincident at least at two points n = j1 and n = j2 such that log j1/ log j2 is irrational, then X follows a Cauchy law. Assuming that condition of coincidence of \bar X(n) and X are fulfilled at least for two n values, but only approximately, with some error ε in metric λ, we prove (without any conditions of symmetry) that, in certain sense, characteristic function of X is close to the characteristic function of the Cauchy distribution.
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| format | Article |
| id | doaj-art-3581f8ecf1534ee0a186794ce4a7e71e |
| institution | Kabale University |
| issn | 0132-2818 2335-898X |
| language | English |
| publishDate | 2023-09-01 |
| publisher | Vilnius University Press |
| record_format | Article |
| series | Lietuvos Matematikos Rinkinys |
| spelling | doaj-art-3581f8ecf1534ee0a186794ce4a7e71e2025-02-11T18:12:25ZengVilnius University PressLietuvos Matematikos Rinkinys0132-28182335-898X2023-09-0146spec.10.15388/LMR.2006.30793On stability estimations without any conditions of symmetryRomanas Januškevičius0Olga Januškevičienė1Institute of Mathematics and InformaticsInstitute of Mathematics and Informatics Let X, X1, X2, ..., Xn be i.i.d. random variables. B. Ramachandran and C.R. Rao have proved that if distributions of sample mean ‾X = ‾X(n) = (X1 + ⋯ + Xn)/n and monomial X are coincident at least at two points n = j1 and n = j2 such that log j1/ log j2 is irrational, then X follows a Cauchy law. Assuming that condition of coincidence of \bar X(n) and X are fulfilled at least for two n values, but only approximately, with some error ε in metric λ, we prove (without any conditions of symmetry) that, in certain sense, characteristic function of X is close to the characteristic function of the Cauchy distribution. https://www.zurnalai.vu.lt/LMR/article/view/30793stability estimationsCauchy distributionsample meanidentically distributed statistics |
| spellingShingle | Romanas Januškevičius Olga Januškevičienė On stability estimations without any conditions of symmetry Lietuvos Matematikos Rinkinys stability estimations Cauchy distribution sample mean identically distributed statistics |
| title | On stability estimations without any conditions of symmetry |
| title_full | On stability estimations without any conditions of symmetry |
| title_fullStr | On stability estimations without any conditions of symmetry |
| title_full_unstemmed | On stability estimations without any conditions of symmetry |
| title_short | On stability estimations without any conditions of symmetry |
| title_sort | on stability estimations without any conditions of symmetry |
| topic | stability estimations Cauchy distribution sample mean identically distributed statistics |
| url | https://www.zurnalai.vu.lt/LMR/article/view/30793 |
| work_keys_str_mv | AT romanasjanuskevicius onstabilityestimationswithoutanyconditionsofsymmetry AT olgajanuskeviciene onstabilityestimationswithoutanyconditionsofsymmetry |