Copyright © 2010 Z. A. Abo-Eleneen and E. M. Nigm. This is an open access article distributed under the
Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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.