Approximate ML Estimation in Type I Generalized Logistic Distribution under Type-II Censoring - Ananthasetty, Vasudeva Rao (Journal of Global Research in Mathematical Archives(JGRMA), 2018)
In two-parameter Type-I generalized logistic distribution (GLD), even in complete samples, the ML equations of scale and shape parameters are to be solved numerically using an iterative technique such as Newton-Raphson method.Â Â Assuming shape parameter is known, based on aÂ Â Â Type-II censored sample, Vasudeva Rao et al. (2017) derived a linear estimator for scale parameter by making linear approximations to the non-linear terms appearing in the ML equation of scale parameter.Â Â They call this new linear estimator as linear approximate MLE (LAMLE).Â But, in all practical situations, we may not assume shape parameter is known.Â Therefore, in this paper, we suggest an iterative procedure to solve the LAMLE of scale parameter and the ML equation of shape parameter jointly to yield some new estimates called as approximate MLEs (AMLEs). Based on a Monte-Carlo simulation study, we compare the AMLEs with the corresponding MLEs and found that the AMLEs are almost as efficient as MLEs.Â However, we restricted our simulation study only for the case of complete sample and left censored samples, because of the non-convergence of the MLEs in case of rightÂ and doubly censored samples. Â Finally, we demonstrate the computation of AMLEs and their comparison with MLEs by means of two real data sets.Â