### Abstract

We consider the problem of estimating the total probability of all symbols that appear with a given frequency in a string of i.i.d. random variables with unknown distribution. We focus on the regime in which the block length is large yet no symbol appears frequently in the string. This is accomplished by allowing the distribution to change with the block length. Under a natural convergence assumption on the sequence of underlying distributions, we show that the total probabilities converge to a deterministic limit, which we characterize. We then show that the Good-Turing total probability estimator is strongly consistent.

Original language | English (US) |
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Title of host publication | Proceedings - 2006 IEEE International Symposium on Information Theory, ISIT 2006 |

Pages | 2526-2530 |

Number of pages | 5 |

DOIs | |

State | Published - 2006 |

Event | 2006 IEEE International Symposium on Information Theory, ISIT 2006 - Seattle, WA, United States Duration: Jul 9 2006 → Jul 14 2006 |

### Publication series

Name | IEEE International Symposium on Information Theory - Proceedings |
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ISSN (Print) | 2157-8101 |

### Other

Other | 2006 IEEE International Symposium on Information Theory, ISIT 2006 |
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Country | United States |

City | Seattle, WA |

Period | 7/9/06 → 7/14/06 |

### All Science Journal Classification (ASJC) codes

- Theoretical Computer Science
- Information Systems
- Modeling and Simulation
- Applied Mathematics

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## Cite this

*Proceedings - 2006 IEEE International Symposium on Information Theory, ISIT 2006*(pp. 2526-2530). [4036427] (IEEE International Symposium on Information Theory - Proceedings). https://doi.org/10.1109/ISIT.2006.262066