An approximate maximum likelihood estimator in a weighted exponential distribution

  • Lee, Jang-Choon (Division of Computer Engineering, Taegu Science University) ;
  • Lee, Chang-Soo (Department of Flight Operation, Kyungwoon University)
  • Received : 2011.12.20
  • Accepted : 2012.01.13
  • Published : 2012.01.31


We derive approximate maximum likelihood estimators of two parameters in a weighted exponential distribution, and derive the density function for the ratio Y=(X+Y) of two independent weighted exponential random variables X and Y, and then observe the skewness of the ratio density.


  1. Abramowitz, M. and Stegun, I. A. (1970). Handbook of mathematical functions, Dover Publications Inc., New York.
  2. Ali, M. M., Pal, M. and Woo, J. (2009). Estimation of P(Y > X) when X and Y belong to different distribution families. Journal of Probability and Statistical Science, 8, 19-33.
  3. Ali, M. M., Woo, J. and Nadarajah, S. (2005). On the ratio X=(X+Y ) for the power function distribution. Pakistan Journal of Statistics, 21, 131-138.
  4. Balakrishnan, N. and Cohen, A. C. (1991). Order statistics and inferences, Academic Press, Inc., New York.
  5. Gradshteyn, I. S. and Ryzhik, I. M. (1965). Tables of integrals, series, and products, Academic Press, New York.
  6. Gupta, R. D. and Kundu, D. (2009). A new class of weighted exponential distributions. Statistics, 43, 621-643.
  7. Lee, J. C. and Lee, C. S. (2010). Reliability and ratio in a right truncated Rayleigh distribution. Journal of the Korean Data & Information Sciences Society, 21, 195-200.
  8. Martz, H. F. and Waller, R. A. (1982). Bayesian reliability analysis, John Wiley & Sons, New York.
  9. Moon, Y. G., Lee, C. S. and Ryu, S. G. (2009). Reliability and ratio in exponentiated complementary power function distribution. Journal of the Korean Data & Information Sciences Society, 20, 955-960.
  10. Pal, M., Ali, M. M. and Woo, J. (2005). Estimation and testing of P(Y > X) in two parameter exponential distributions. Statistics, 39, 415-428.
  11. Raqab, M., Ahmadi, J. and Doostparast, M. (2007). Statistical inference based on record data from Pareto model. Statistics, 41, 105-108
  12. Rohatgi, V. K. (1976). An introduction to probability theory and mathematical statistics, John Wiley & Sons, New York.
  13. Son, H. and Woo, J. (2009). Estimations in a skewed double Weibull distribution. Communications of the Korean Statistical Society, 16, 859-870.
  14. Woo, J. (2008). Estimating reliability and distribution of ratio in two independent different variates. Journal of the Korean Data & Information Science Society, 19, 967-977.

Cited by

  1. Simulation study on the estimation of multinomial proportions vol.23, pp.2, 2012,
  2. Estimation of the exponential distribution based on multiply Type I hybrid censored sample vol.25, pp.3, 2014,
  3. Estimations of the skew parameter in a skewed double power function distribution vol.24, pp.4, 2013,
  4. Estimation for the Rayleigh distribution based on Type I hybrid censored sample vol.25, pp.2, 2014,
  5. Reliability estimation and ratio distribution in a general exponential distribution vol.25, pp.3, 2014,