Partial generalized probability weighted moments for exponentiated exponential distribution

  • Authors

    • Amal Hassan Cairo University
    • El Sayed Elsherpieny Cairo University
    • Neema El Haroun Cairo Uiversity
  • The generalized probability weighted moments are widely used in hydrology for estimating parameters of flood distributions from complete sample. The method of partial generalized probability weighted moments was used to estimate the parameters of distributions from censored sample. This article offers new method called partial generalized probability weighted moments (PGPWMs) for the analysis of censored data. The method of PGPWMs is an extended class from partial generalized probability weighted moments. To illustrate the new method, estimation of the unknown parameters from exponentiated exponential distribution based on doubly censored sample is considered. PGPWMs estimators for right and left censored samples are obtained as special cases. Simulation study is conducted to investigate performance of estimates for exponentiated exponential distribution. Comparison between estimators is made through simulation via their biases and mean square errors. An illustration with real data is provided.

    Keywords: Generalized Probability Weighted Moments, Partial Probability Weighted Moments, Partial Generalized Probability Weighted Moments, Generalized Exponential Distribution, and Censored Samples.

  • References

    1. Gupta, R.D. and Kundu, D. (1999). Generalized exponential distributions, Australian and New Zealand Journal of Statistics, 41(2), 173-188.
    2. Wang, Q.J. (1990a). Estimation of the GEV distribution from censored samples by method of partial probability weighted moments, Journal of Hydrology, 120(1-4), 103-114.
    3. Wang, Q. J., (1990b) "Unbiased estimation of probability weighted moments and partial probability weighted moments from systematic and historical flood information and their application to estimating the GEV distribution". Journal of Hydrology 120, 115–124.
    4. Wang, Q. J., (1996). “Using partial probability weighted moments to fit the extreme value distributions to censored samples". Water Resources Research, 32(6), 1767–1771.
    5. Zafirakou-Koulouris, A., Vogel, R.M., Craig, S., M., Habermier, J., (1998) “L-moment Diagram for Censored Observation" Water Resources Research, 34, (5), 1241–1249.
    6. Deng, J. and Pandey, M.D., (2009) “Using Partial Probability Weighted Moments and Partial Maximum entropy to estimate Quantiles from Censored Samples" Probabilistic Engineering Mechanics, 24, 407- 417.
    7. Rasmussen, P. (2001)."Generalized Probability Weighted Moment: Application to the Generalized Pareto Distribution". Water Resources Research, 37, 6, 1745-1751.
    8. Hosking, J. R. M. (1986) "The Theory of Probability Weighted Moments". Research Report RC 12210, IBM Research Division, Yorktown Heights, NY.
    9. Al-Khodary, E., Hassan, A., and Allam, S. (2008). Double Censoring Partial Probability Weighted Moments Estimation of the Generalized Exponential Distribution, InterStat, pp. 1–24.
    10. El Haroun, N.M. (2009).”Generalized Probability Weighted Moments Estimators for Some Distributions". M.Sc. Thesis, Cairo University.
    11. Al-Khodary, E., Hassan, A., and Allam, S. (2007). Self-determinant probability weighted moment’s method for estimating the parameters of the generalized exponential distribution. Proceeding of the 19st Annual Conference Statistics and Computer Modeling in Human and Social Sciences, Faculty of Economics and Political Science, Cairo University. 19, 159-176.
    12. Lawless, J. F. (1982), Statistical Models and Methods for Lifetime Data, John Wiley & Sons, New York.
  • Downloads

  • How to Cite

    Hassan, A., Elsherpieny, E. S., & El Haroun, N. (2014). Partial generalized probability weighted moments for exponentiated exponential distribution. International Journal of Basic and Applied Sciences, 3(3), 234-244.