• A. Vasudeva Rao

For the logistic distribution, the maximum likelihood (ML) method does not yield explicit estimators for the location and scale parameters based on Type II censored samples. To address this, Balakrishnan(1992) derived the approximate MLEs (AMLEs) of the parameters, which are in non-linear form. In this paper, we construct some new AMLEs by making linear approximations to the intractable terms of the ML equations using least squares method, a new approach of linearization. Since, the new AMLEs are in linear form, we call them as linear AMLEs (LAMLEs). A Monte Carlo simulation study is made to investigate the performance of LAMLEs, as compared with MLEs and Balakrishnan’s AMLEs; and we found that the LAMLEs are almost as efficient as MLEs and AMLEs. However, the LAMLEs are slightly biased than both MLEs and AMLEs. Further, we compare unbiased LAMLEs with the corresponding BLUEs based on the exact variances of the estimators and interestingly, these new unbiased LAMLEs are found just as efficient as the BLUEs in both complete and Type-II censored samples even in small samples. However, the construction of unbiased LAMLEs require only the means of order statistics of standard logistic distribution where as the construction of BLUEs require means as well as the variances and covariances of order statistics. Finally, we present some numerical examples to illustrate the construction of the new estimators developed here.

Location and scale parameters of logistic distribution; Type-II censoring; Least squares method; Linear approximate MLEs; Unbiased linear approximate MLEs.

"Efficient Linear Approximate ML Estimation for the Logistic Distribution under Type-II Censoring", International Journal of Emerging Technologies and Innovative Research (www.jetir.org), ISSN:2349-5162, Vol.6, Issue 4, page no.548-565, April-2019, Available :http://www.jetir.org/papers/JETIR1904696.pdf

"Efficient Linear Approximate ML Estimation for the Logistic Distribution under Type-II Censoring", International Journal of Emerging Technologies and Innovative Research (www.jetir.org | UGC and issn Approved), ISSN:2349-5162, Vol.6, Issue 4, page no. pp548-565, April-2019, Available at : http://www.jetir.org/papers/JETIR1904696.pdf