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Bivariate Exponential Distributions
Abstract
A bivariate distribution is not determined by the knowledge of the margins. Two bivariate distributions with exponential margins are analyzed and another is briefly mentioned. In the first distribution (2.1) the conditional expectation of one variable decreases to zero with increasing values of the other one. The coefficient of correlation is never positive and lies in the interval –.40≤ρ≤0, and the correlation ratio varies from –.48 to zero. In the second distribution (3.4) the conditional expectation of one variable increases or decreases with increasing values of the other variable depending on the sign of the correlation. The coefficient of correlation lies in the interval –.25≤ρ≤.25, and the correlation ratio is proportional to the coefficient.
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Cited by
Regression analysis of multivariate incomplete failure time data by modeling marginal distributions
Wei, L. J., Lin, D. Y., & Weissfeld, L. (1989) · Journal of the American Statistical Association · doi:10.1080/01621459.1989.10478873 · Cited by 1,868
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
Multivariate hydrological frequency analysis using copulas
Favre, A., El Adlouni, S., Perreault, L., Thiémonge, N., & Bobée, B. (2004) · Water Resources Research · doi:10.1029/2003wr002456 · Cited by 696
A Conditional Approach for Multivariate Extreme Values (with Discussion)
Heffernan, J. E., & Tawn, J. A. (2004) · Journal of the Royal Statistical Society Series B: Statistical Methodology · doi:10.1111/j.1467-9868.2004.02050.x · Cited by 677
Enjoy the Joy of Copulas: With a Package copula
Yan, J. (2007) · Journal of Statistical Software · doi:10.18637/jss.v021.i04 · Cited by 502
Metadata
- Authors
- Gumbel, E. J.
- Venue
- Journal of the American Statistical Association
- Publisher
- Informa UK Limited
- Published
- 1960-12
- Volume
- 55
- Issue
- 292
- Pages
- 698-707
- ISSN
- 0162-1459 (ISSN-L)
- 1537-274X
- OpenAlex
- W2158114082
- Cited by
- 1,321
- References
- 0
- FWCI
- 1.41
- Type
- journal article
- Language
- en
- Open access
- closed
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