Sum of Bernoulli Mixtures: Beyond Conditional Independence
We consider the distribution of the sum of Bernoulli mixtures under a general dependence structure. The level of dependence is measured in terms of a limiting conditional correlation between two of the Bernoulli random variables. The conditioning event is that the mixing random variable is larger th...
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | Journal of Probability and Statistics |
| Online Access: | http://dx.doi.org/10.1155/2014/838625 |
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| author | Taehan Bae Ian Iscoe |
| author_facet | Taehan Bae Ian Iscoe |
| author_sort | Taehan Bae |
| collection | DOAJ |
| description | We consider the distribution of the sum of Bernoulli mixtures under a general dependence structure. The level of dependence is measured in terms of a limiting conditional correlation between two of the Bernoulli random variables. The conditioning event is that the mixing random variable is larger than a threshold and the limit is with respect to the threshold tending to one. The large-sample distribution of the empirical frequency and its use in approximating the risk measures, value at risk and conditional tail expectation, are presented for a new class of models which we call double mixtures. Several illustrative examples with a Beta mixing distribution, are given. As well, some data from the area of credit risk are fit with the models, and comparisons are made between the new models and also the classical Beta-binomial model. |
| format | Article |
| id | doaj-art-282805724f5348fda9e386cb5a1df255 |
| institution | Kabale University |
| issn | 1687-952X 1687-9538 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Probability and Statistics |
| spelling | doaj-art-282805724f5348fda9e386cb5a1df2552025-02-03T06:00:18ZengWileyJournal of Probability and Statistics1687-952X1687-95382014-01-01201410.1155/2014/838625838625Sum of Bernoulli Mixtures: Beyond Conditional IndependenceTaehan Bae0Ian Iscoe1Department of Mathematics and Statistics, University of Regina, Regina, SK, S4S 0A2, CanadaQuantitative Research, Risk Analytics, IBM Corporation, 185 Spadina Avenue, Toronto, ON, M5T 2C6, CanadaWe consider the distribution of the sum of Bernoulli mixtures under a general dependence structure. The level of dependence is measured in terms of a limiting conditional correlation between two of the Bernoulli random variables. The conditioning event is that the mixing random variable is larger than a threshold and the limit is with respect to the threshold tending to one. The large-sample distribution of the empirical frequency and its use in approximating the risk measures, value at risk and conditional tail expectation, are presented for a new class of models which we call double mixtures. Several illustrative examples with a Beta mixing distribution, are given. As well, some data from the area of credit risk are fit with the models, and comparisons are made between the new models and also the classical Beta-binomial model.http://dx.doi.org/10.1155/2014/838625 |
| spellingShingle | Taehan Bae Ian Iscoe Sum of Bernoulli Mixtures: Beyond Conditional Independence Journal of Probability and Statistics |
| title | Sum of Bernoulli Mixtures: Beyond Conditional Independence |
| title_full | Sum of Bernoulli Mixtures: Beyond Conditional Independence |
| title_fullStr | Sum of Bernoulli Mixtures: Beyond Conditional Independence |
| title_full_unstemmed | Sum of Bernoulli Mixtures: Beyond Conditional Independence |
| title_short | Sum of Bernoulli Mixtures: Beyond Conditional Independence |
| title_sort | sum of bernoulli mixtures beyond conditional independence |
| url | http://dx.doi.org/10.1155/2014/838625 |
| work_keys_str_mv | AT taehanbae sumofbernoullimixturesbeyondconditionalindependence AT ianiscoe sumofbernoullimixturesbeyondconditionalindependence |