| Title:
|
Bounds on tail probabilities for negative binomial distributions (English) |
| Author:
|
Harremoës, Peter |
| Language:
|
English |
| Journal:
|
Kybernetika |
| ISSN:
|
0023-5954 (print) |
| ISSN:
|
1805-949X (online) |
| Volume:
|
52 |
| Issue:
|
6 |
| Year:
|
2016 |
| Pages:
|
943-966 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this paper we derive various bounds on tail probabilities of distributions for which the generated exponential family has a linear or quadratic variance function. The main result is an inequality relating the signed log-likelihood of a negative binomial distribution with the signed log-likelihood of a Gamma distribution. This bound leads to a new bound on the signed log-likelihood of a binomial distribution compared with a Poisson distribution that can be used to prove an intersection property of the signed log-likelihood of a binomial distribution compared with a standard Gaussian distribution. All the derived inequalities are related and they are all of a qualitative nature that can be formulated via stochastic domination or a certain intersection property. (English) |
| Keyword:
|
tail probability |
| Keyword:
|
exponential family |
| Keyword:
|
signed log-likelihood |
| Keyword:
|
variance function |
| Keyword:
|
inequalities |
| MSC:
|
60E15 |
| MSC:
|
60F10 |
| MSC:
|
62E17 |
| idZBL:
|
Zbl 06707382 |
| idMR:
|
MR3607856 |
| DOI:
|
10.14736/kyb-2016-6-0943 |
| . |
| Date available:
|
2017-02-13T11:47:13Z |
| Last updated:
|
2018-01-10 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/145999 |
| . |
| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
[6] Harremoës, P.: Mutual information of contingency tables and related inequalities..In: Proc. ISIT 2014, IEEE 2014, pp. 2474-2478. 10.1109/isit.2014.6875279 |
| Reference:
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[7] Harremoës, P., Tusnády, G.: Information divergence is more $\chi^2$-distributed than the $\chi^2$-statistic..In: International Symposium on Information Theory (ISIT 2012) (Cambridge, Massachusetts), IEEE 2012, pp. 538-543. 10.1109/isit.2012.6284247 |
| Reference:
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| . |
