Journal of the Korean Data and Information Science Society

The Korean Data and Information Science Society (한국데이터정보과학회)
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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
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Abstract

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.

Keywords

References

  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. https://doi.org/10.1080/02331880802605346
  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. https://doi.org/10.1080/02331880500274031
  11. Raqab, M., Ahmadi, J. and Doostparast, M. (2007). Statistical inference based on record data from Pareto model. Statistics, 41, 105-108 https://doi.org/10.1080/02331880601106579
  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. https://doi.org/10.5351/CKSS.2009.16.5.859
  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.

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