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Sequential Analysis
Design Methods and Applications
Volume 43, 2024 - Issue 1
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Research Articles

Estimation of fixed-accuracy confidence interval of the stress–strength reliability for inverse Pareto distribution using two-stage sampling technique

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Pages 79-102 | Received 21 Jun 2023, Accepted 04 Nov 2023, Published online: 10 Jan 2024

REFERENCES

  • Anscombe, F. J. 1952. “Large-Sample Theory of Sequential Estimation.” Mathematical Proceedings of the Cambridge Philosophical Society 48 (4):600–7. https://doi.org/10.1017/S0305004100076386
  • Asgharzadeh, A., S. Nadarajah, and F. Sharafi. 2017. “Generalized Inverse Lindley Distribution with Application to Danish Fire Insurance Data.” Communications in Statistics - Theory and Methods 46 (10):5001–21. https://doi.org/10.1080/03610926.2015.1096394
  • Bain, L., and M. Englehardt. 1991. Statistical Analysis of Reliability and Life-Testing Models: Theory and Methods. Vol. 115. New York: CRC Press.
  • Banerjee, S., and N. Mukhopadhyay. 2016. “A General Sequential Fixed-Accuracy Confidence Interval Estimation Methodology for a Positive Parameter: Illustrations Using Health and Safety Data.” Annals of the Institute of Statistical Mathematics 68 (3):541–70. https://doi.org/10.1007/s10463-015-0504-2
  • Bapat, S. R. 2018. “Purely Sequential Fixed Accuracy Confidence Intervals for P(X<Y) under Bivariate Exponential Models.” American Journal of Mathematical and Management Sciences 37 (4):386–400. https://doi.org/10.1080/01966324.2018.1465867
  • Bapat, S. R., N. Joshi, and A. K. Shukla. 2023. “On Fixed-Accuracy Confidence Intervals for the Parameters of Lindley Distribution and Its Extensions.” Austrian Journal of Statistics 52 (2):104–15. https://doi.org/10.17713/ajs.v52i2.1406
  • Beg, M. A. 1980. “On the Estimation of Pr(Y>X) for the Two-Parameter Exponential Distribution.” Metrika 27 (1):29–34. https://doi.org/10.1007/BF01893574
  • Bennett, Steve. 1983. “Log-Logistic Regression Models for Survival Data.” Applied Statistics 32 (2):165–71. https://doi.org/10.2307/2347295
  • Birnbaum, Z. W. 1956. “On a Use of the Mann–Whitney Statistic.” In Proceedings of the Third Berkeley Symposium on Mathematical Statistics and Probability. Vol. 1, edited by J. Neyman, Contributions to the Theory of Statistics, 13–7. Berkeley: University of California Press.
  • Birnbaum, Z. W., and R. C. McCarty. 1958. “A Distribution-Free Upper Confidence Bound for P(Y>X), Based on Independent Samples of X and Y.” The Annals of Mathematical Statistics 29 (2):558–62. https://doi.org/10.1214/aoms/1177706631
  • Cha, J. H., S. Lee, and J. Jeon. 2006. “Sequential Confidence Interval Estimation for System Availability.” Quality and Reliability Engineering International 22 (2):165–76. https://doi.org/10.1002/qre.693
  • Chaturvedi, A., and S. K. Tomer. 2003. “UMVU Estimation of the Reliability Function of the Generalized Life Distributions.” Statistical Papers 44 (3):301–13. https://doi.org/10.1007/s00362-003-0157-8
  • Church, J. D., and B. Harris. 1970. “The Estimation of Reliability from Stress-Strength Relationship.” Technometrics 12 (1):49–54. https://doi.org/10.1080/00401706.1970.10488633
  • Constantine, K., M. Karson, and S. K. Tse. 1986. “Estimators of P(Y<X) in the Gamma Case.” Communications in Statistics - Simulation and Computation 15 (2):365–88. https://doi.org/10.1080/03610918608812513
  • Dankunprasert, S., U. Jaroengeratikun, and T. Talangtam. 2021. “The Properties of Inverse Pareto Distribution and Its Application to Extreme Events.” Thailand Statistician 19 (1):1–12.
  • Ghosh, M., N. Mukhopadhyay, and P. K. Sen. 1997. Sequential Estimation. New York: Wiley.
  • Govindarajulu, Z. 1967. “Two Sided Confidence Limits for P(X>Y) Based on Normal Samples of X and Y.” Sankhya B 29 (1–2):35–40.
  • Guo, L., and W. Gui. 2018. “Bayesian and Classical Estimation of the Inverse Pareto Distribution and Its Application Strength-Stress Models.” American Journal of Mathematical and Management Sciences 37 (1):80–92. https://doi.org/10.1080/01966324.2017.1383217
  • Holmberg, P. 2009. “Supply Function Equilibria of Pay-as-Bid Auctions.” Journal of Regulatory Economics 36 (2):154–77. https://doi.org/10.1007/s11149-009-9091-6
  • Hu, J., Y. Zhuang, and C. Goldiner. 2021. “Fixed-Accuracy Confidence Interval Estimation of P(X<Y) under a Geometric-Exponential Model.” Japanese Journal of Statistics and Data Science 4 (2):1079–104. https://doi.org/10.1007/s42081-021-00122-2
  • Ivshin, V. V., and Y. P. Lumelskii. 1995. Statistical Estimation Problems in Stress-Strength Models. Russia: Perm University Press.
  • Johnson, R. A. 1988. “Stress-Strength Models for Reliability.” In Handbook of Statistics. Vol. 7, edited by P. R. Krishnaiah and C. R. Rao, 27–54. North Holland: Elsevier.
  • Khalifeh, A., E. Mahmoudi, and A. Chaturvedi. 2020. “Sequential Fixed-Accuracy Confidence Intervals for the Stress-Strength Reliability Parameter for the Exponential Distribution: Two-Stage Sampling Procedure.” Computational Statistics 35 (4):1553–75. https://doi.org/10.1007/s00180-020-00957-5
  • Kotz, S., Y. Lumelskii, and M. Pensky. 2003. The Stress-Strength Model and Its Generalizations, Theory and Applications. Singapore: World Scientific.
  • Kundu, D., and R. D. Gupta. 2006. “Estimation of P(Y<X) for Weibull Distributions.” IEEE Transactions on Reliability 55 (2):270–80. https://doi.org/10.1109/TR.2006.874918
  • Langlands, A., S. Pocock, G. Kerr, and S. Gore. 1997. “Long-Term Survival of Patients with Breast Cancer: A Study of the Curability of the Disease.” British Medical Journal 2 (6200):1247–51. https://doi.org/10.1136/bmj.2.6200.1247
  • Mahmoudi, E., A. Khalifeh, and V. Nekoukhou. 2019. “Minimum Risk Sequential Point Estimation of the Stress–Strength Reliability Parameter for Exponential Distribution.” Sequential Analysis 38 (3):279–300. https://doi.org/10.1080/07474946.2019.1649347
  • Mukhopadhyay, N., and S. Banerjee. 2014. “Purely Sequential and Two Stage Fixed-Accuracy Confidence Interval Estimation Methods for Count Data for Negative Binomial Distributions in Statistical Ecology: One-Sample and Two-Sample Problems.” Sequential Analysis 33 (2):251–85. https://doi.org/10.1080/07474946.2014.896701
  • Mukhopadhyay, N., and S. Banerjee. 2015. “Purely Sequential Negative Binomial Problems and Statistical Ecology: A Selected Review with New Directions.” Statistical Methodology 26:34–60. https://doi.org/10.1016/j.stamet.2015.02.006
  • Mukhopadhyay, N., and B. M. de Silva. 2009. Sequential Methods and Their Applications. Boca Raton, FL: CRC.
  • Mukhopadhyay, N., and Y. Zhuang. 2016. “On Fixed-Accuracy and Bounded Accuracy Confidence Interval Estimation Problems in Fisher’s Nile Example.” Sequential Analysis 35 (4):516–35. https://doi.org/10.1080/07474946.2016.1238264
  • Naghettini, M., K. W. Potter, and T. Illangasekare. 1996. “Estimating the Upper Tail of Flood-Peak Frequency Distributions Using Hydrometeorological Information.” Water Resources Research 32 (6):1729–40. https://doi.org/10.1029/96WR00200
  • Patowary, A. N., J. Hazarika, and G. L. Sriwastav. 2013. “Interference Theory of Reliability: A Review.” International Journal of System Assurance Engineering and Management 4 (2):146–58. https://doi.org/10.1007/s13198-013-0162-9
  • Sathe, Y. S., and S. P. Shah. 1981. “On Estimating P(X>Y) for the Exponential Distribution.” Communications in Statistics - Theory and Methods 10 (1):39–47. https://doi.org/10.1080/03610928108828018
  • Sharma, V. K., S. K. Singh, and U. Singh. 2014. “A New Upside-down Bathtub Shaped Hazard Rate Model for Survival Data Analysis.” Applied Mathematics and Computation 239:242–53. https://doi.org/10.1016/j.amc.2014.04.048
  • Sharma, V. K., S. K. Singh, U. Singh, and V. Agiwal. 2015. “The Inverse Lindley Distribution: A Stress-Strength Reliability Model with Application to Head and Neck Cancer Data.” Journal of Industrial and Production Engineering 32 (3):162–73. https://doi.org/10.1080/21681015.2015.1025901
  • Stein, C. 1945. “A Two Sample Test for a Linear Hypothesis Whose Power is Independent of the Variance.” The Annals of Mathematical Statistics 16 (3):243–58. https://doi.org/10.1214/aoms/1177731088
  • Stein, C. 1949. “Some Problems in Sequential Estimation (Abstract).” Econometrica 17:77–8.
  • Tomer, S. K., and M. S. Panwar. 2020. “A Review on Inverse Maxwell Distribution with Its Statistical Properties and Applications.” Journal of Statistical Theory and Practice 14 (3), Article no. 33. https://doi.org/10.1007/s42519-020-00100-z
  • Tong, H. 1974. “A Note on the Estimation of P(Y<X) in the Exponential Case.” Technometrics 16 (4):625.
  • Zhuang, Y., J. Hu, and Y. Zou. 2020. “Fixed-Accuracy Confidence Interval Estimation of P(X>c) for a Two-Parameter Gamma Population.” Communications for Statistical Applications and Methods 27 (6):625–639. https://doi.org/10.29220/CSAM.2020.27.6.625

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