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A Multivariate Exponential Distribution
Abstract
A number of multivariate exponential distributions are known, but they have not been obtained by methods that shed light on their applicability. This paper presents some meaningful derivations of a multivariate exponential distribution that serves to indicate conditions under which the distribution is appropriate. Two of these derivations are based on “shock models,” and one is based on the requirement that residual life is independent of age. It is significant that the derivations all lead to the same distribution. For this distribution, the moment generating function is obtained, comparison is made with the case of independence, the distribution of the minimum is discussed, and various other properties are investigated. A multivariate Weibull distribution is obtained through a change of variables.
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Citations
Cited by
The Analysis of Failure Times in the Presence of Competing Risks
Prentice, R. L., Kalbfleisch, J. D., Peterson, A. V., Flournoy, N., Farewell, V. T., & Breslow, N. E. (1978) · Biometrics · doi:10.2307/2530374 · Cited by 1,266
Understanding Relationships Using Copulas
Frees, E. W., & Valdez, E. A. (1998) · North American Actuarial Journal · doi:10.1080/10920277.1998.10595667 · Cited by 1,257
Association of Random Variables, with Applications
Esary, J. D., Proschan, F., & Walkup, D. W. (1967) · The Annals of Mathematical Statistics · doi:10.1214/aoms/1177698701 · Cited by 1,223
Fault Tree Analysis, Methods, and Applications ߝ A Review
Lee, W. S., Grosh, D. L., Tillman, F. A., & Lie, C. H. (1985) · IEEE Transactions on Reliability · doi:10.1109/tr.1985.5222114 · Cited by 678
An Empirical Analysis of the Pricing of Collateralized Debt Obligations
LONGSTAFF, F. A., & RAJAN, A. (2008) · The Journal of Finance · doi:10.1111/j.1540-6261.2008.01330.x · Cited by 299
Metadata
- Authors
- Marshall, A. W., & Olkin, I.
- Venue
- Journal of the American Statistical Association
- Publisher
- Informa UK Limited
- Published
- 1967-03
- Volume
- 62
- Issue
- 317
- Pages
- 30-44
- ISSN
- 0162-1459 (ISSN-L)
- 1537-274X
- OpenAlex
- W2072430699
- Cited by
- 1,582
- References
- 0
- FWCI
- 8.26
- Type
- journal article
- Language
- en
- Open access
- closed
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- Marshall, A. W., & Olkin, I. (1967). A Multivariate Exponential Distribution. Journal of the American Statistical Association. https://doi.org/10.1080/01621459.1967.10482885
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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.
