Hostname: page-component-cd9895bd7-dzt6s Total loading time: 0 Render date: 2024-12-28T03:32:45.648Z Has data issue: false hasContentIssue false
  • English
  • Français

Probability Density Function of the Product and Quotient of Two Correlated Exponential Random Variables

Published online by Cambridge University Press:  20 November 2018

Henrick J. Malik  and
Roger Trudel
Henrick J. Malik
Affiliation:
University of Guelph Guelph, Ontario
Roger Trudel
Affiliation:
Agriculture Canada Ottawa, Ontario
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

This article deals with the distributions of the product and the quotient of two correlated exponential random variables. We consider here three types of bivariate exponential distributions: Marshall-Olkin's bivariate exponential distribution, Gumbel's Type I bivariate exponential distribution, and Gumbel's Type II bivariate exponential distribution.

Keywords

62E15.
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 29 , Issue 4 , 01 December 1986 , pp. 413 - 418
Copyright
Copyright © Canadian Mathematical Society 1986

References

1. Basu, A. P. and Block, H. W. (1975). On characterizing univariate and multivariate exponential distributions with applications. In a modern course on statistical distribution in scientific work (G. Patil, P., et al. editors). Reidel Publishing Company, Holland.Google Scholar
2. Cherian, K. C. (1941). A bivariate correlated gamma type distribution function. Journal of the Indian Mathematical Society, 5, 133–144.Google Scholar
3. Donahue, J. D. (1964). Products and quotients of random variables and their applications. Office of Aerospace Research, U.S.A.F. Google Scholar
4. Downton, F. (1970). Bivariate exponential distributions in reliability theory. Journal of the Royal Statistical Society, Series B, 32, 408–417.Google Scholar
5. Gradshteyn, I. S. and Ryzhik, I. M. (1965). Table of integrals, series, and products, fourth edition. Academic Press, Inc.: New York, London.Google Scholar
6. Gulati, L. (1970). On the distributions of the products of order statistics. (Abstract) Annals of mathematical statistics, 41, p. 1156.Google Scholar
7. Gumbel, E. J. (1958). Statistics of Extremes. Columbia University Press: New York, London.Google Scholar
8. Gumbel, E. J. (1960). Bivariate exponential distributions. Journal of the American Statistical Association, 55, 698–707.Google Scholar
9. Gupta, S. S. (1965). On some multiple decision (selection and ranking) rules. Technometrics, 7, 225–245.Google Scholar
10. Johnson, N. L. and Kotz, S. (1972). Distributions in statistics: Continuous multivariate distributions. John Wiley & Sons, New York.Google Scholar
11. Kibble, W. F. (1941). A two-variate gamma type distribution. Sankhya, 5, 137–150.Google Scholar
12. Lomnicki, Z. A. (1967). On the distribution of products of random variables. Journal of the Royal Statistical Society, Series B, 29, 513–524.Google Scholar
13. Malik, H. J. (1967). Exact distribution of the quotient of independent generalized gamma random variâtes. Canadian Mathematical Bulletin, 10, pp. 463—465.Google Scholar
14. Malik, H. J. (1968). Exact distribution of the product of two generalized gamma variâtes. Annals of Mathematical Statistics, 39, 1751–1752.Google Scholar
15. Mardia, K. V. (1970). Families of Bivariate Distributions. Hafner Publishing Company: Darien, Connecticut.Google Scholar
16. Marshall, A. W. and Olkin, I. (1967). A multivariate exponential distribution. Journal of the American Statistical Association, 62, 30–44.Google Scholar
17. Morgenstern, D. (1956). Einfache Beispiele zweidimensionaler Vertelungen. Miteilungsblatt Fur Mathematische Statistik, 8, 234–235.Google Scholar
18. Springer, M. D. and Thompson, W. E. (1964). The distribution of products of independent random variables. General Motors Defense Research Laboratories, Mathematics and Evaluation Studies Department: Santa Barbara, California.Google Scholar
19. Springer, M. D. and Thompson, W. E. (1966). The distribution of product of independent random variables. S.I.A.M. Journal of Applied Mathematics, 14, 511–526.Google Scholar
20. Springer, M. D. (1979). The Algebra of Random Variables. John Wiley and Sons, New York.Google Scholar
21. Stacy, E. W. and Mihram, G. A. (1965). Parameter estimation for a generalized gamma distribution. Technometrics, 7, 349–358.Google Scholar