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

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Keywords

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