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Estimation of the Parameters of the Reversed Generalized Logistic Distribution with Progressive Censoring Data

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  • Z. A. Abo-Eleneen
  • E. M. Nigm

Abstract

The reversed generalized logistic (RGL) distributions are very useful classes of densities as they posses a wide range of indices of skewness and kurtosis. This paper considers the estimation problem for the parameters of the RGL distribution based on progressive Type II censoring. The maximum likelihood method for RGL distribution yields equations that have to be solved numerically, even when the complete sample is available. By approximating the likelihood equations, we obtain explicit estimators which are in approximation to the MLEs. Using these approximate estimators as starting values, we obtain the MLEs using iterative method. We examine numerically MLEs estimators and the approximate estimators and show that the approximation provides estimators that are almost as efficient as MLEs. Also we show that the value of the MLEs decreases as the value of the shape parameter increases. An exact confidence interval and an exact joint confidence region for the parameters are constructed. Numerical example is presented in the methods proposed in this paper.

Suggested Citation

  • Z. A. Abo-Eleneen & E. M. Nigm, 2010. "Estimation of the Parameters of the Reversed Generalized Logistic Distribution with Progressive Censoring Data," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2010, pages 1-21, January.
    • Handle: RePEc:hin:jijmms:539860
    DOI: 10.1155/2010/539860
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