Expectation thinning operators based on linear fractional probability generating functions
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2017
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| _version_ | 1866911749491392512 |
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| author | Aly, Emad-Eldin A. A. Bouzar, Nadjib |
| author_facet | Aly, Emad-Eldin A. A. Bouzar, Nadjib |
| contents | We introduce a two-parameter expectation thinning operator based on a linear fractional probability generating function. The operator is then used to define a first-order integer-valued autoregressive \inar1 process. Distributional properties of the \inar1 process are described. We revisit the Bernoulli-geometric \inar1 process of Bourguignon and Weiß (2017) and we introduce a new stationary \inar1 process with a compound negative binomial distribution. Lastly, we show how a proper randomization of our operator leads to a generalized notion of monotonicity for distributions on \bzp. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1709_03129 |
| institution | arXiv |
| publishDate | 2017 |
| record_format | arxiv |
| spellingShingle | Expectation thinning operators based on linear fractional probability generating functions Aly, Emad-Eldin A. A. Bouzar, Nadjib Probability 60E05 60E10 62M10 We introduce a two-parameter expectation thinning operator based on a linear fractional probability generating function. The operator is then used to define a first-order integer-valued autoregressive \inar1 process. Distributional properties of the \inar1 process are described. We revisit the Bernoulli-geometric \inar1 process of Bourguignon and Weiß (2017) and we introduce a new stationary \inar1 process with a compound negative binomial distribution. Lastly, we show how a proper randomization of our operator leads to a generalized notion of monotonicity for distributions on \bzp. |
| title | Expectation thinning operators based on linear fractional probability generating functions |
| topic | Probability 60E05 60E10 62M10 |
| url | https://arxiv.org/abs/1709.03129 |