### Abstract

Necessary and sufficient conditions are presented for sums of asymptotically independent random variables to converge to a normal random variable in the sense of total variation distance, uniform metric for characteristic functions, and mean metric of order q.

Original language | English |
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Pages (from-to) | 3002-3004 |

Number of pages | 3 |

Journal | Journal of Mathematical Sciences |

Volume | 91 |

Issue number | 3 |

Publication status | Published - 1998 |

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### ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics
- Statistics and Probability

### Cite this

*Journal of Mathematical Sciences*,

*91*(3), 3002-3004.

**The central limit theorem without the condition of independence.** / Szeidl, L.; Zolotarev, V. M.

Research output: Contribution to journal › Article

*Journal of Mathematical Sciences*, vol. 91, no. 3, pp. 3002-3004.

}

TY - JOUR

T1 - The central limit theorem without the condition of independence

AU - Szeidl, L.

AU - Zolotarev, V. M.

PY - 1998

Y1 - 1998

N2 - Necessary and sufficient conditions are presented for sums of asymptotically independent random variables to converge to a normal random variable in the sense of total variation distance, uniform metric for characteristic functions, and mean metric of order q.

AB - Necessary and sufficient conditions are presented for sums of asymptotically independent random variables to converge to a normal random variable in the sense of total variation distance, uniform metric for characteristic functions, and mean metric of order q.

UR - http://www.scopus.com/inward/record.url?scp=54749095995&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=54749095995&partnerID=8YFLogxK

M3 - Article

VL - 91

SP - 3002

EP - 3004

JO - Journal of Mathematical Sciences

JF - Journal of Mathematical Sciences

SN - 1072-3374

IS - 3

ER -