Studies on generalized Yule models
We present a generalization of the Yule model for macroevolution in which, for the appearance of genera, we consider point processes with the order statistics property, while for the growth of species we use nonlinear time-fractional pure birth processes or a critical birth-death process. Further, i...
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| Format: | Article |
| Language: | English |
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VTeX
2018-12-01
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| Series: | Modern Stochastics: Theory and Applications |
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| Online Access: | https://www.vmsta.org/doi/10.15559/18-VMSTA125 |
| _version_ | 1818020220442247168 |
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| author | Federico Polito |
| author_facet | Federico Polito |
| author_sort | Federico Polito |
| collection | DOAJ |
| description | We present a generalization of the Yule model for macroevolution in which, for the appearance of genera, we consider point processes with the order statistics property, while for the growth of species we use nonlinear time-fractional pure birth processes or a critical birth-death process. Further, in specific cases we derive the explicit form of the distribution of the number of species of a genus chosen uniformly at random for each time. Besides, we introduce a time-changed mixed Poisson process with the same marginal distribution as that of the time-fractional Poisson process. |
| first_indexed | 2024-04-14T08:02:00Z |
| format | Article |
| id | doaj.art-35bfac72839c4224934e46b1f9b68697 |
| institution | Directory Open Access Journal |
| issn | 2351-6046 2351-6054 |
| language | English |
| last_indexed | 2024-04-14T08:02:00Z |
| publishDate | 2018-12-01 |
| publisher | VTeX |
| record_format | Article |
| series | Modern Stochastics: Theory and Applications |
| spelling | doaj.art-35bfac72839c4224934e46b1f9b686972022-12-22T02:04:52ZengVTeXModern Stochastics: Theory and Applications2351-60462351-60542018-12-0161415510.15559/18-VMSTA125Studies on generalized Yule modelsFederico Polito0Dipartimento di Matematica, Università di Torino, Via Carlo Alberto 10, 10123, Torino, ItalyWe present a generalization of the Yule model for macroevolution in which, for the appearance of genera, we consider point processes with the order statistics property, while for the growth of species we use nonlinear time-fractional pure birth processes or a critical birth-death process. Further, in specific cases we derive the explicit form of the distribution of the number of species of a genus chosen uniformly at random for each time. Besides, we introduce a time-changed mixed Poisson process with the same marginal distribution as that of the time-fractional Poisson process.https://www.vmsta.org/doi/10.15559/18-VMSTA125Yule modelmixed Poisson processestime-fractional Poisson processorder statistics property |
| spellingShingle | Federico Polito Studies on generalized Yule models Modern Stochastics: Theory and Applications Yule model mixed Poisson processes time-fractional Poisson process order statistics property |
| title | Studies on generalized Yule models |
| title_full | Studies on generalized Yule models |
| title_fullStr | Studies on generalized Yule models |
| title_full_unstemmed | Studies on generalized Yule models |
| title_short | Studies on generalized Yule models |
| title_sort | studies on generalized yule models |
| topic | Yule model mixed Poisson processes time-fractional Poisson process order statistics property |
| url | https://www.vmsta.org/doi/10.15559/18-VMSTA125 |
| work_keys_str_mv | AT federicopolito studiesongeneralizedyulemodels |