Estimating the parameter of the Lindley distribution under progressive type-II censored data


We consider the estimation problem of the Lindley distribution based on progressive type-II censored data. We use the EM algorithm for estimating the involved parameter using the maximum likelihood method. The asymptotic variance of the MLE within the EM framework is obtained. Then, the asymptotic confidence intervals of the parameter are constructed. Finally, a real data set and a simulation study are presented to illustrate the obtained results.

DOI Code: 10.1285/i20705948v8n1p100

Keywords: EM algorithm, Lindley distribution, Maximum likelihood estimators, Progressively type-II censoring


bibitem{1} Al-Zahrani, B., $&$ Gindwan, M. (2014). Parameter estimation of a two-parameter Lindley distribution under hybrid censoring. {em International Journal of Systems Assurance Engineering and Management}. DOI:10.1007/s13198-013-0213-2.

bibitem{2} Balakrishnan, N., $&$ Aggarwala, R. (2000). Progressive Censoring: Theory, Methods and. Applications. Boston: Birkh"auser.

bibitem{3} Dempster, A. P., Laird, N. M., $&$ Rubin, D. B. (1977). Maximum likelihood from incomplete data via the EM algorithm. {em Journal of the Royal Statistical Society}, 39, 1--38.

bibitem{4} Geddes, K. O., Glasser, M. L., Moore, R. A., $&$ Scott, T. C. (1990). Evaluation of classes of definite integrals involving elementary functions via differentiation of special functions. {em Applicable Algebra in Engineering, Communication and Computing}, 1, 149--165.

bibitem{5} Ghitany, M. E., Alqallaf, F., Al-Mutairi, D. K., $&$ Husain, H. A. (2011). A two-parameter weighted Lindley distribution and its applications to survival data. {em Mathematics and Computers in Simulation}, 81, 1190--1201.

bibitem{6} Ghitany, M. E., Atieh, B., $&$ Nadarajah, S. (2008). Lindley distribution and its application. {em Mathematics and Computers in Simulation}, 78, 493--506.

bibitem{66} Louis, T. A. (1982). Finding the observed information matrix using the EM algorithm, {em Journal of the Royal Statistical Society}, 44, 226--233.

bibitem{7} McLachlan, G. J., $&$ Krishnan, T. (2008). The EM Algorithm and Extensions, Second Edition. Hoboken, New Jersey: John Wiley and Sons.

bibitem{8} Ng, H. K. T., Chan, P. S., $&$ Balakrishnan, N. (2002). Estimation of parameters from progressively censored data using EM algorithm. {em Computational Statistics $&$ Data Analysis}, 39, 371--386.

bibitem{9} Sarhan, A. M., $&$ Abuammoh, A. (2008). Statistical Inference Using Progressively Type-II Censored Data with Random Scheme, {em International Mathematical Forum}, 35, 1713--1725.

bibitem{10} Shanker, R., Sharma, S., $&$ Shanker, R. (2013). A Two-Parameter Lindley Distribution for Modeling Waiting and Survival Times Data, {em Applied Mathematics}, 4, 363--368.

bibitem{11} Robert, C. P., $&$ Casella, G. (2005). Monte Carlo Statistical Methods. Secaucus, New Jersey: Springer-Verlag New York, Inc.

bibitem{13} Zakerzadeh, H., $&$ Mahmoudi, E. (2012). A new two parameter lifetime distribution: model and properties. {arXiv preprint arXiv:1204.4248}.

Full Text: pdf

Creative Commons License
This work is licensed under a Creative Commons Attribuzione - Non commerciale - Non opere derivate 3.0 Italia License.