Recurrence Relations for Moments of Order Statistics from the Lindley Distribution with General Multiply Type-II Censored Sample

Bander Al-Zahrani, M A Ali


In this paper, we derive the recurrence relations for the moments of function of single and two order statistics from Lindley distribution. We also consider the maximum likelihood estimation (MLE) of the parameter of the distribution based on multiply type-II censoring. However maximum likelihood estimator does not have an explicit form for the involved parameter. In order to compute the MLE of the parameter, Monte Carlo simulation is used. A comparative study is presented between classical MLE and MLE from multiply type-II censored sample.


Ali, M.A. and Khan, A.H. (1998a). Recurrence relations for the expectations of a function of single order statistic from general class of distributions, Journal of the Indian Statistical Association, Vol. 35, pp. 1--9.

Ali, M.A. and Khan, A.H. (1998b). Recurrence relations for expected values of certain functions of two order statistics, Metron, Vol. LVI, n.1-2, pp. 107--119.

David, H.A. and Nagaraja, H.N. (2003). Order Statistics, 3rd. ed. Wiley, N.Y., USA.

Ghitany, M.E., Atieh, B. and Nadarajah, S. (2008). Lindley distribution and its application, Mathematics and computers in simulation, Vol. 78, pp. 493--506.

Jang, D., Park, J. and Kim, C. (2011). Estimation of the scale parameter of the half-logistic distribution with multiply type-II censored sample, Journal of the Korean Statistical Society, Vol. 40, pp. 291--301.

Kong, F. and Fei, H. (1996). Limit theorems for the maximum likelihood estimate under general multiply type-II censoring, Annals of the Institute of Statistical Mathematics, vol. 48, pp. 731--755.

Lindley, D.V. (1952). Fiducial distributions and Bayes' theorem, Journal of the Royal Statistical Society, Series B, Vol. 20, pp. 102--107.

Schenk, N.; Burkschat, M.; Cramer, E. and Kamps, U.(2011). Bayesian estimation and prediction with multiply Type-II censored samples of sequential order statistics from one- and two-parameter exponential distributions, Journal of Statistical Planning and Inference, Vol. 141, pp. 1575--1587.

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DOI: 10.19139/soic.v2i2.55


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