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Relations for moments of progressively Type-II censored order statistics from half-logistic distribution with applications to inference

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  • Balakrishnan, N.
  • Saleh, H.M.

Abstract

In this paper, we establish several recurrence relations for the single and product moments of progressively Type-II right censored order statistics from a half-logistic distribution. The use of these relations in a systematic recursive manner would enable one to compute all the means, variances and covariances of progressively Type-II right censored order statistics from the half-logistic distribution for all sample sizes n, effective sample sizes m, and all progressive censoring schemes (R1,...,Rm). The results established here generalize the corresponding results for the usual order statistics due to Balakrishnan (1985). These moments are then utilized to derive best linear unbiased estimators of the scale and location-scale parameters of the half-logistic distribution. A comparison of these estimators with the maximum likelihood estimates is then made. The best linear unbiased predictors of censored failure times is then discussed briefly. Finally, two numerical examples are presented to illustrate all the inferential methods developed here.

Suggested Citation

  • Balakrishnan, N. & Saleh, H.M., 2011. "Relations for moments of progressively Type-II censored order statistics from half-logistic distribution with applications to inference," Computational Statistics & Data Analysis, Elsevier, vol. 55(10), pages 2775-2792, October.
    • Handle: RePEc:eee:csdana:v:55:y:2011:i:10:p:2775-2792
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    References listed on IDEAS

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    1. Ng, H. K. T. & Chan, P. S. & Balakrishnan, N., 2002. "Estimation of parameters from progressively censored data using EM algorithm," Computational Statistics & Data Analysis, Elsevier, vol. 39(4), pages 371-386, June.
    2. Fischer, T. & Balakrishnan, N. & Cramer, E., 2008. "Mixture representation for order statistics from INID progressive censoring and its applications," Journal of Multivariate Analysis, Elsevier, vol. 99(9), pages 1999-2015, October.
    3. N. Balakrishnan, 2007. "Progressive censoring methodology: an appraisal," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 16(2), pages 211-259, August.
    4. Balakrishnan, N. & Chan, P. S., 1992. "Estimation for the scaled half logistic distribution under Type II censoring," Computational Statistics & Data Analysis, Elsevier, vol. 13(2), pages 123-141, March.
    5. Chansoo Kim & Keunhee Han, 2010. "Estimation of the scale parameter of the half-logistic distribution under progressively type II censored sample," Statistical Papers, Springer, vol. 51(2), pages 375-387, June.
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    Cited by:

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    2. Abdulhamid A. Alzaid & Weaam M. Alhadlaq, 2023. "A New Family of Archimedean Copulas: The Half-Logistic Family of Copulas," Mathematics, MDPI, vol. 12(1), pages 1-18, December.
    3. Jung-In Seo & Suk-Bok Kang, 2016. "An objective Bayesian analysis of the two-parameter half-logistic distribution based on progressively type-II censored samples," Journal of Applied Statistics, Taylor & Francis Journals, vol. 43(12), pages 2172-2190, September.
    4. Bander Al-Zahrani & Areej M. AL-Zaydi, 2022. "Moments of progressively type-II censored order statistics from the complementary exponential geometric distribution and associated inference," International Journal of System Assurance Engineering and Management, Springer;The Society for Reliability, Engineering Quality and Operations Management (SREQOM),India, and Division of Operation and Maintenance, Lulea University of Technology, Sweden, vol. 13(3), pages 1052-1065, June.
    5. Devendra Kumar & Mazen Nassar & Mansoor Rashid Malik & Sanku Dey, 2023. "Estimation of the Location and Scale Parameters of Generalized Pareto Distribution Based on Progressively Type-II Censored Order Statistics," Annals of Data Science, Springer, vol. 10(2), pages 349-383, April.
    6. Seo, Jung-In & Kang, Suk-Bok, 2015. "Pivotal inference for the scaled half logistic distribution based on progressively Type-II censored samples," Statistics & Probability Letters, Elsevier, vol. 104(C), pages 109-116.
    7. Mansour Shrahili & Naif Alotaibi & Devendra Kumar & Salem A. Alyami, 2020. "Inference for the Two Parameter Reduced Kies Distribution under Progressive Type-II Censoring," Mathematics, MDPI, vol. 8(11), pages 1-20, November.
    8. Jeon, Young Eun & Kang, Suk-Bok, 2020. "Estimation for the half-logistic distribution based on multiply Type-II hybrid censoring," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 550(C).
    9. Malik Mansoor Rashid & Kumar Devendra, 2017. "Relations for Moments of Progressively Type-II Right Censored Order Statistics From Erlang-Truncated Exponential Distribution," Statistics in Transition New Series, Statistics Poland, vol. 18(4), pages 651-668, December.
    10. Mansoor Rashid Malik & Devendra Kumar, 2017. "Relations For Moments Of Progressively Type-Ii Right Censored Order Statistics From Erlang-Truncated Exponential Distribution," Statistics in Transition New Series, Polish Statistical Association, vol. 18(4), pages 651-668, December.

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