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Estimation for the three-parameter lognormal distribution based on progressively censored data

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  • Basak, Prasanta
  • Basak, Indrani
  • Balakrishnan, N.

Abstract

Some work has been done in the past on the estimation of parameters of the three-parameter lognormal distribution based on complete and censored samples. In this article, we develop inferential methods based on progressively Type-II censored samples from a three-parameter lognormal distribution. In particular, we use the EM algorithm as well as some other numerical methods to determine maximum likelihood estimates (MLEs) of parameters. The asymptotic variances and covariances of the MLEs from the EM algorithm are computed by using the missing information principle. An alternative estimator, which is a modification of the MLE, is also proposed. The methodology developed here is then illustrated with some numerical examples. Finally, we also discuss the interval estimation based on large-sample theory and examine the actual coverage probabilities of these confidence intervals in case of small samples by means of a Monte Carlo simulation study.

Suggested Citation

  • Basak, Prasanta & Basak, Indrani & Balakrishnan, N., 2009. "Estimation for the three-parameter lognormal distribution based on progressively censored data," Computational Statistics & Data Analysis, Elsevier, vol. 53(10), pages 3580-3592, August.
    • Handle: RePEc:eee:csdana:v:53:y:2009:i:10:p:3580-3592
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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. 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.
    3. Balakrishnan, N. & Mi, Jie, 2003. "Existence and uniqueness of the MLEs for normal distribution based on general progressively Type-II censored samples," Statistics & Probability Letters, Elsevier, vol. 64(4), pages 407-414, October.
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    3. Tian, Yuzhu & Zhu, Qianqian & Tian, Maozai, 2015. "Estimation for mixed exponential distributions under type-II progressively hybrid censored samples," Computational Statistics & Data Analysis, Elsevier, vol. 89(C), pages 85-96.
    4. Refah Alotaibi & Mazen Nassar & Hoda Rezk & Ahmed Elshahhat, 2022. "Inferences and Engineering Applications of Alpha Power Weibull Distribution Using Progressive Type-II Censoring," Mathematics, MDPI, vol. 10(16), pages 1-21, August.
    5. Kotb, M.S. & Raqab, M.Z., 2019. "Statistical inference for modified Weibull distribution based on progressively type-II censored data," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 162(C), pages 233-248.
    6. Wang, HaiYing & Flournoy, Nancy, 2015. "On the consistency of the maximum likelihood estimator for the three parameter lognormal distribution," Statistics & Probability Letters, Elsevier, vol. 105(C), pages 57-64.
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    9. Krishna, Hare & Kumar, Kapil, 2011. "Reliability estimation in Lindley distribution with progressively type II right censored sample," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 82(2), pages 281-294.
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