The DOI matches its Crossref record; 7 of the 7 references it cites were found in a registry or an index.
A use of complex probabilities in the theory of stochastic processes
Abstract
The exponential distribution is very important in the theory of stochastic processes with discrete states in continuous time. A. K. Erlang suggested a method of extending to other distributions methods that apply in the first instance only to exponential distributions. His idea is generalized to cover all distributions with rational Laplace transforms; this involves the formal use of complex transition probabilities. Properties of the method are considered.
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Citations
Cites
An introduction to probability theory and its applications
(1958) · Journal of the Franklin Institute · doi:10.1016/0016-0032(58)90688-4 · Cited by 29,269
Titchmarsh, E. C. (1932) · BURJC Digital (King Juan Carlos University) · Cited by 2,290
An Introduction to Probability Theory and its Applications.
Kendall, D. G., & Feller, W. (1951) · Journal of the Royal Statistical Society. Series A (General) · doi:10.2307/2980979 · Cited by 1,283
Fisher, A., Whittaker, E. T., & Blackie, G. R. (1924) · Journal of the American Statistical Association · doi:10.2307/2277387 · Cited by 731
ON THE ROLE OF VARIABLE GENERATION TIME IN THE DEVELOPMENT OF A STOCHASTIC BIRTH PROCESS
KENDALL, D. G. (1948) · Biometrika · doi:10.1093/biomet/35.3-4.316 · Cited by 199
On the Choice of a Mathematical Model to Represent Normal Bacterial Growth
Kendall, D. G. (1952) · Journal of the Royal Statistical Society Series B (Statistical Methodology) · doi:10.1111/j.2517-6161.1952.tb00100.x · Cited by 54
Bartlett, M. S. (1945) · Mathematical Proceedings of the Cambridge Philosophical Society · doi:10.1017/s0305004100022398 · Cited by 52
Cited by
Marshall, A. H., & McClean, S. I. (2004) · Health Care Management Science · doi:10.1007/s10729-004-7537-z · Cited by 86
Metadata
- Authors
- Cox, D. R.
- Venue
- Mathematical Proceedings of the Cambridge Philosophical Society
- Publisher
- Cambridge University Press (CUP)
- Published
- 1955-04
- Volume
- 51
- Issue
- 2
- Pages
- 313-319
- ISSN
- 0305-0041 (ISSN-L)
- 1469-8064
- OpenAlex
- W2147607210
- Cited by
- 580
- References
- 7
- FWCI
- 0.87
- Type
- journal article
- Language
- en
- Open access
- closed
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Data sources
Bibliographic data: Semantic Scholar, OpenAlex, Crossref.
Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.
