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ISSN: 1549-3644 (Print)
ISSN: 1558-6359 (Online)
Research Article Open Access

Random Sum of Mixtures of Sum of Bivariate Exponential Distributions

Abd El-Moneim A.M. Teamah and Ahmed M.T. Abd El-Bar

Abstract

Problem statement: The distributions of R = X+Y and W = X/(X+Y), where X and Y follow Lawrance and Lewis`s bivariate exponential distribution, is generalized. Approach: In this research we found mixtures of sum of bivariate exponential random variables. Results: Also we calculated the probability density function (pdf) of the random sum of mixtures of sum of bivariate exponential random variables. Conclusion/Recommendations: In this study we investigated the pdf of random sum of mixtures of sum of bivariate exponential random variables.

Journal of Mathematics and Statistics
Volume 5 No. 4, 2009, 270-275

DOI: https://doi.org/10.3844/jmssp.2009.270.275

Submitted On: 18 January 2008 Published On: 31 December 2009

How to Cite: Teamah, A. E. A. & El-Bar, A. M. A. (2009). Random Sum of Mixtures of Sum of Bivariate Exponential Distributions. Journal of Mathematics and Statistics, 5(4), 270-275. https://doi.org/10.3844/jmssp.2009.270.275

Open AccessCopyright: © 2009 Abd El-Moneim A.M. Teamah and Ahmed M.T. Abd El-Bar. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

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Keywords

  • Lawrance and Lewis’s bivariate exponential distribution
  • random sum
  • mixture distribution
  • Laplace transform