Approximate ML Estimation in Type I Generalized Logistic Distribution under Type-II Censoring

Vasudeva Rao Ananthasetty

Abstract


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.   Assuming shape parameter is known, based on a    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.   They call this new linear estimator as linear approximate MLE (LAMLE).  But, in all practical situations, we may not assume shape parameter is known.  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.  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 right  and doubly censored samples.  Finally, we demonstrate the computation of AMLEs and their comparison with MLEs by means of two real data sets. 

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References


. Abushal, T.A. (2013). On Bayesian prediction of future median generalized order statistics using doubly censored data from Type-I generalized logistic model, Journal of Statistical and Econometric Methods. 2, 61-79

. Alkasasbeh, M.R., Raqab, M.Z. (2009). Estimation of the generalized logistic distribution parameters, comparative study, Statistical Methodology. 6, 262-279.

. Amin, E.A.(2012a). Bayesian and Non-Bayesian Estimation of P(Y

. Amin, E.A. (2012b). The sampling distribution of the maximum likelihood estimators from Type I generalized distribution based on lower record values, Int. J. Contemp. Math. Sciences. 7, 1205-1212.

. Azzalini, A. (1985). A Class of distributions which includes the normal ones, Scandinavian Journal of Statistics, 12, 171-178.

. Asgharzadeh, A. (2006). Point and interval estimation for a generalized logistic distribution under progressively Type II censoring, Communications in Statistics – Theory and Methods, 35, 1685-1702.

. Badar, M.G. and Priest, A.M.(1982). Statistical Aspects of Fiber and Bundle Strength in Hybrids Composites. In: Hayashi, T., Kawata, K., Umekawa, S. eds. Progress in Science and Engineering Composites, ICCM-IV. Tokyo, 1129-1136.

. Balakrishnan, N. (1990). Approximate maximum likelihood estimation for a generalized logistic distribution., J.Statist. Planning and Inference. 26, 221 – 236.

. Balakrishnan, N., Ed. (1992). Handbook of the Logistic distribution. New York: Marcel Dekker.

. Balakrishnan, N. and Leung, M.Y. (1988a). Order statistics from type I generalized logistic distribution, Communications in Statistics – Simulation and Computation, 17, 25 – 50.

. Balakrishnan, N. and Leung, M.Y. (1988b). Means, Variances and Covariances of order statistics, best linear unbiased estimates for the type I generalized logistic distribution and some applications, Communications in Statistics – Simulation and Computation, 17, 51 – 84.

. Bernardo, J.M. (1976). Algorithm As 103:Psi (Digamma) function, Journal of the Royal statistical society series C. 25, 315-317.

. Lagos-Alvarez, B., Jimernez-Gamerro, M.D., Alba-Fernandez,V. (2011). Bias correction in the Type I generalized logistic distribution, Communications in Statistics – Simulation and Computation, 40, 511-531.

. Lloyd,E.H. (1952). Least squares estimation of location and scale parameters using order statistics. Biometrika, 1952, 39, 88- 95.

. Murali Krishna, E., Kantam R.R.L., and Vasudeva Rao, A., (1993). Linear estimation in Type I generalized logistic distribution, Proceedings of II Annual Conference of S D S, 45-55.

. Olapade, A.K. (2000). Some properties of the Type I Generalized Logistic Distribution. Inter stat, 2.

. Sreekumar, N.V., Thomas, P.Y. (2008). Estimation of the parameters of Type I generalized logistic distribution using order statistics, Communications in Statistics – Theory and Methods, 37, 1506-1524.

. Shao, Q. (2002). Maximum likelihood estimation for generalized logistic distribution. Communications in Statistics – Theory and Methods, 31, 1687-1700.

. Vasudeva Rao, A., Sitaramacharyulu, P. and Chenchuramaiah, M. (2017). Linear approximate ML estimation in scaled Type I generalized logistic distribution based on Type-II censored samples, Communications in Statistics – Simulation and Computation, 46, 1682 – 1702.


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