Approximate maximum likelihood estimation for a generalized logistic distribution

For the Type-I generalized logistic distribution, the maximum likelihood method does not provide explicit estimators for the location and scale parameters based on either complete or Type-II censored samples. We present a simple method of deriving explicit estimators by approximating the likelihood equations appropriately. We derive approximate expressions for the variances and covariance of these estimators. We also show that these estimators are just as efficient as the best linear unbiased estimators (BLUE's). Finally, we illustrate this method of estimation by considering an example.