Journals / Gazi University Journal of Science / 2012 / Cilt: 25 - Sayı: 2

In this paper, a progressive type I group-censoring life test for Burr XII distribution is considered. We use the maximum likelihood method to obtain the point estimators of the Burr XII parameters. The approximate confidence intervals for the parameters

Yunus AKDOĞAN1,♠, Coşkun KUŞ2, Shuo-Jye WU3

Pages
425–434
Publication Date
2012-04-16
DOI
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

The sensitivity analysis is also investigated.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:Öz In this paper, a progressive type I group-censoring life test for Burr XII distribution is considered.
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Key Findings & Data:We use modified algorithm proposed by Kus et al. [19] to decide the number of test units, number of inspections, and length of inspection interval under a restricted budget of experiment such that the determinant of the asymptotic variances-covariance of estimators of parameters is minimum.
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Conclusion & Impact:The sensitivity analysis is also investigated.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Anahtar Kelimeler D-Optimality · Grouped data · Interval censoring

Özet

Öz In this paper, a progressive type I group-censoring life test for Burr XII distribution is considered. We use the maximum likelihood method to obtain the point estimators of the Burr XII parameters. The approximate confidence intervals for the parameters of Burr XII distribution are also obtained. We use modified algorithm proposed by Kus et al. [19] to decide the number of test units, number of inspections, and length of inspection interval under a restricted budget of experiment such that the determinant of the asymptotic variances-covariance of estimators of parameters is minimum. A numerical example is presented to illustrate the proposed approach. The sensitivity analysis is also investigated.

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Cite This Article

KUS, C., WU, S., AKDOGAN, Y. (2012). In this paper, a progressive type I group-censoring life test for Burr XII distribution is considered. We use the maximum likelihood method to obtain the point estimators of the Burr XII parameters. The approximate confidence intervals for the parameters. Gazi University Journal of Science, Cilt: 25 - Sayı: 2, 425–434. https://ajindex.com/articles/255319

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References (13)

  1. Aggarwala, R. “Progressive interval censoring: some mathematical results with applications to inference” Communications in Statistics - Theory and Methods, 30, 1921-1935 (2001).
  2. Akdoğan, Y., “Progressively group censoring and optimal design of experiment”, Selçuk University Science Institute published Master Thesis, Konya (2011).
  3. Akdoğan, Y., Kuş, C. “Kısıtlı Maliyet Durumunda Burr Tip III Dağılımı için Optimal İlerleyen Tür Grup Sansürleme Planı”, Uluslararası 7. İstatistik Kongresi, Antalya, 28 Nisan-01 Mayıs 2011., 4(1): 210-211 (2011).
  4. Akdoğan, Y., Kuş, C., Wu, S.-J. “Optimal progressive group-censoring plans for Logistic distribution under cost constraint “, 5th Annual International Statistics & Mathematical Education, Athens, Greece, 13-16 June 2011, MAT2011/3379 (2011). on Mathematics, AL-Hussaini, E.K., Jaheen, Z.F., Bayesian prediction bounds for the Burr type XII failure model, Communications in Statistics - Theory and Methods, 24 (7): 1829–1842 (1995).
  5. AL-Hussaini, E.K., Jaheen, Z.F “Bayesian prediction bounds for the Burr type XII distribution in the presence of outliers”, J. Statist. Planning Inference, 23–37, 55 (1996).
  6. Ali Mousa, M.A.M., Jaheen, Z.F., “Bayesian prediction for the Burr type XII model based on doubly censored data”, Statistics 29, 285–294 (1997).
  7. Ali Mousa, M.A.M., Jaheen, Z.F., “Bayesian prediction for the two parameter Burr type XII model based on doubly censored data”, J. Appl. Statist. Sci. 7 (2/3),103–111 (1998).
  8. Ali Mousa, M.A.M., Jaheen, Z.F., “Statistical inference progressively censored data”, Comput. Math. Appl. 43, 1441–1449 (2002). model based on Ali Mousa, M.A.M., Jaheen, Z.F., “Bayesian prediction for progressively censored data form the Burr model”, Statist. Papers 43, 587–593 (2002).
  9. Burr, I. W. Cumulative frequency functions. Annals of Mathematical Statistics, 13, 215–232 (1942).
  10. Burr, I.W., Cislak, P.J., “On a general system of distributions: I. Its curve-shape characteristics: II. The sample median”, J. Am. Statist. Assoc. 63, 627–635 (1968).
  11. Casella, G., Berger, R. L. “Statistical Inference”, 2nd edition, Duxbury, Pacafic Grove, CA. Chen, Z. “A new two-parameter lifetime distribution with bathtub shape or increasing failure rate function”, Statistics and Probability Letters, 49, 155-161 (2000).
  12. Chen, Z., Mi, J. “Confidence interval for the mean of the exponential distribution, Based on grouped data”. IEEE Transactions on Reliability, 45, 671-677 (1996).
  13. Cheng, K. F., Chen, C. H. “Estimation of the Weibull