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Estimation procedures for Maxwell distribution under type-I progressive hybrid censoring scheme. (English) Zbl 1457.62323
Summary: The Maxwell (or Maxwell-Boltzmann) distribution was invented to solve the problems relating to physics and chemistry. It has also proved its strength of analysing the lifetime data. For this distribution, we consider point and interval estimation procedures in the presence of type-I progressively hybrid censored data. We obtain maximum likelihood estimator of the parameter and provide asymptotic and bootstrap confidence intervals of it. The Bayes estimates and Bayesian credible and highest posterior density intervals are obtained using inverted gamma prior. The expression of the expected number of failures in life testing experiment is also derived. The results are illustrated through the simulation study and analysis of a real data set is presented.

MSC:
62N05 Reliability and life testing
62F10 Point estimation
62F15 Bayesian inference
Software:
bootstrap
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[1] Johnson NL, Kotz S, Balakrishnan N. Continuous univariate distributions. Vol. 1 New York: Wiley; 1994. [Google Scholar] · Zbl 0811.62001
[2] Krishna H, Malik M. Relaibility estimation of Maxwell distribution with type-II censored data. Int J Qual Reliab Manag. 2009;26:184-195. doi: 10.1108/02656710910928815[Crossref], [Google Scholar]
[3] Tyagi RK, Bhattacharya SK. Bayes estimation of the Maxwell’s velocity distribution function. Statistica. 1989;29:563-567. [Google Scholar] · Zbl 0718.62068
[4] Tyagi RK, Bhattacharya SK. A note on the MVU estimation of reliability for the Maxwell failure distribution. Estadistica. 1989;41:73-79. [Google Scholar]
[5] Chaturvedi A, Rani U. Classical and Bayesian reliability estimation of the generalized Maxwell failure distribution. J Statist Res. 1998;32:113-120. [Google Scholar]
[6] Bekker A, Roux JJ. Reliability characteristics of the Maxwell distribution: a Bayes estimation study. Comm Stat. (Theory Meth) 2005;34:2169-2178. doi: 10.1080/STA-200066424[Taylor & Francis Online], [Web of Science ®], [Google Scholar] · Zbl 1081.62087
[7] Krishna H, Malik M. Reliability estimation in Maxwell distribution with progressively type-II censored data. J Statist Comput Simul. 2012;82:623-641. doi: 10.1080/00949655.2010.550291[Taylor & Francis Online], [Web of Science ®], [Google Scholar] · Zbl 1318.62310
[8] Balakrishnan N, Aggarwala R. Progressive censoring: theory, methods and applications. Boston: Birkhauser; 2000. [Crossref], [Google Scholar]
[9] Kundu D, Jordar A. Analysis of type-II progressively hybrid censored data. Comput Stat Data Anal. 2006;50:2509-2528. doi: 10.1016/j.csda.2005.05.002[Crossref], [Web of Science ®], [Google Scholar] · Zbl 1284.62605
[10] Childs A, Chandrasekar B, Balakrishnan N. Exact likelihood inference for an exponential parameter under progressive hybrid censoring. In: Vonta F, Nikulin M, Limnios N, Huber-Carol C, editors. Statistical models and methods for biomedical and technical systems. Boston: Birkhauser; 2008. p. 319-330. [Crossref], [Google Scholar] · Zbl 1049.62021
[11] Balakrishnan N, Kundu D. Hybrid censoring: models, inferential results and applications. Comput Stat Data Anal. 2012;57:166-209. doi: 10.1016/j.csda.2012.03.025[Crossref], [Web of Science ®], [Google Scholar] · Zbl 1365.62364
[12] Lin CT, Chou CC, Huang YL. Inference for the Weibull distribution with progressive hybrid censoring. Comput Stat Data Anal. 2012;56:451-467. doi: 10.1016/j.csda.2011.09.002[Crossref], [Web of Science ®], [Google Scholar] · Zbl 1316.62042
[13] Gradshteyn IS, Ryzhik IM. Tables of integrals, series and products. New York: Academic Press; 1965. [Google Scholar]
[14] Efron B, Tibshirani RJ. An introduction to the bootstrap. New York: Chapman & Hall; 1993 doi: 10.1007/978-1-4899-4541-9[Crossref], [Google Scholar] · Zbl 0835.62038
[15] Lindley DV. Approximate Bayesian methods. Trabajos Estadistica. 1980;31:223-237. doi: 10.1007/BF02888353[Crossref], [Google Scholar] · Zbl 0458.62002
[16] Chen MH, Shao QM, Ibrahim JG. Monte carlo methods in Bayesian computation. New York: Springer-Verlag; 2000. [Crossref], [Google Scholar] · Zbl 0949.65005
[17] Chen MH, Shao QM. Monte carlo estimation of Bayesian credible and HPD interval. J Comput Graph Stat. 1999;8:69-92. [Taylor & Francis Online], [Web of Science ®], [Google Scholar]
[18] Kamps U, Cramer E. On distributions of generalized order statistics. Statistics. 2001;35:269-280. doi: 10.1080/02331880108802736[Taylor & Francis Online], [Web of Science ®], [Google Scholar] · Zbl 0979.62036
[19] Lawless JF. Statistical models and methods for lifetime data. 2nd ed.New York: John Wiley & Sons; 2003. [Google Scholar] · Zbl 1015.62093
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