Event count distributions from renewal processes: fast computation of probabilities
| Autor: | Rose Baker, Tarak Kharrat |
|---|---|
| Rok vydání: | 2016 |
| Předmět: |
FOS: Computer and information sciences
Class (set theory) statistics methodology Discretization Exploit Computer science Strategy and Management Computation Event count 0211 other engineering and technologies Richardson extrapolation 02 engineering and technology Management Science and Operations Research computer.software_genre 01 natural sciences Management Information Systems Methodology (stat.ME) 010104 statistics & probability 0101 mathematics Statistics - Methodology Flexibility (engineering) 021103 operations research Applied Mathematics Distribution (mathematics) Modeling and Simulation bepress|Physical Sciences and Mathematics|Statistics and Probability Data mining General Economics Econometrics and Finance computer Algorithm |
| Zdroj: | IMA Journal of Management Mathematics |
| ISSN: | 1471-678X |
| DOI: | 10.48550/arxiv.1610.06157 |
| Popis: | Discrete distributions derived from renewal processes, ie distributions of the number of events by some time t are beginning to be used in econometrics and health sciences. A new fast method is presented for computation of the probabilities for these distributions. We calculate the count probabilities by repeatedly convolving the discretized distribution, and then correct them using Richardson extrapolation. When just one probability is required, a second algorithm is described, an adaptation of De Pril's method, in which the computation time does not depend on the ordinality, so that even high-order probabilities can be rapidly found. Any survival distribution can be used to model the inter-arrival times, which gives a rich class of models with great flexibility for modelling both underdispersed and overdispersed data. This work could pave the way for the routine use of these distributions as an additional tool for modelling event count data. An empirical example using fertility data illustrates the use of the method and was fully implemented using an R package Countr developed by the authors and available from the Comprehensive R Archive Network. Comment: 20 pages, 6 figures |
| Databáze: | OpenAIRE |
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