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BLOCK AND BASU'S BIVARIATE EXPONENTIAL DISTRIBUTION WITH APPLICATION TO DROUGHT DATA

Published online by Cambridge University Press:  15 December 2006

Saralees Nadarajah
Affiliation:
School of Mathematics, University of Manchester, Manchester M13 9PL, UK, E-mail: saralees.nadarajah@manchester.ac.uk
Samuel Kotz
Affiliation:
Department of Engineering Management and Systems Engineering, George Washington University, Washington, DC 20052, E-mail: kotz@seas.gwu.edu

Abstract

Motivated by hydrological applications, the exact distributions of R = X + Y, P = XY, and W = X/(X + Y) and the corresponding moment properties are derived when X and Y follow Block and Basu's bivariate exponential distribution. An application of the results is provided to drought data from Nebraska.

Type
Research Article
Copyright
© 2007 Cambridge University Press

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References

REFERENCES

Block, H.W. & Basu, A.P. (1974). A continuous bivariate exponential distribution. Journal of the American Statistical Association 69: 10311037.Google Scholar
Dennis, J.E. & Schnabel, R.B. (1983). Numerical methods for unconstrained optimization and nonlinear equations. Englewood Cliffs, NJ: Prentice-Hall.
Gradshteyn, I.S. & Ryzhik, I.M. (2000). Table of integrals, series, and products, 6th ed. San Diego: Academic Press.
Gumbel, E.J. (1960). Bivariate exponential distributions. Journal of the American Statistical Association 55: 698707.Google Scholar
Ihaka, R. & Gentleman, R. (1996). R: A language for data analysis and graphics, Journal of Computational and Graphical Statistics 5: 299314.Google Scholar
Marshall, A.W. & Olkin, I. (1967). A multivariate exponential distribution. Journal of the American Statistical Association 62: 3044.Google Scholar
Prudnikov, A.P., Brychkov, Y.A., & Marichev, O.I. (1986). Integrals and series, Vols. 1–3. Amsterdam: Gordon & Breach Science.
Schnabel, R.B., Koontz, J.E., & Weiss, B.E. (1985). A modular system of algorithms for unconstrained minimization, ACM Transactions on Mathematical Software 11: 419440.Google Scholar
Yevjevich, V. (1967). An objective approach to definitions and investigations of continental hydrologic droughts. Hydrologic Paper No. 23, Colorado State University, Fort Collins.