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Article

On comparing locations of two-parameter exponential distributions using sequential sampling with applications in cancer research

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Pages 6114-6135 | Received 30 Jan 2020, Accepted 04 Jul 2020, Published online: 21 Jul 2020

References

  • Balakrishnan, N., and A. P. Basu. 1995. The exponential distribution: Theory. In Methods and applications. Amsterdam: Gordon and Breach.
  • Banerjee, A., U. B. Chitnis, S. L. Jadhav, J. S. Bhawalkar, and S. Chaudhury. 2009. Hypothesis testing, type I and type II errors. Industrial Psychiatry Journal 18 (2):127–31. doi:10.4103/0972-6748.62274.
  • Basu, A. P. 1971. On a sequential rule for estimating the location parameter of an exponential distribution. Naval Research Logistics Quarterly 18 (3):329–37. doi:10.1002/nav.3800180305.
  • Bayoud, H. A., and O. A. Kittaneh. 2016. Testing the equality of two exponential distributions. Communications in Statistics - Simulation and Computation 45 (7):2249–56. doi:10.1080/03610918.2014.895837.
  • Chow, Y. S., and H. Robbins. 1965. On the asymptotic theory of fixed width sequential confidence intervals for the mean. Annals of Mathematical Statistics 36:457–62.
  • Efron, B. 1988. Logistic regression, survival analysis, and the Kaplan-Meier curve. Journal of the American Statistical Association 83 (402):414–25. doi:10.1080/01621459.1988.10478612.
  • Ghosh, B. K., and P. K. Sen. 1991. Handbook of sequential analysis, edited volume. New York: Dekker.
  • Ghosh, M., and N. Mukhopadhyay. 1979. Sequential point estimation of the mean when the distribution is unspecified. Communications in Statistics, Theory and Methods 8:637–52.
  • Ghosh, M., and N. Mukhopadhyay. 1981. Consistency and asymptotic efficiency of two stage and sequential estimation procedures. Sankhyā: The Indian Journal of Statistics, Series A (1961–2002) 43:220–27.
  • Ghosh, M., N. Mukhopadhyay, and P. K. Sen. 1997. Sequential estimation. New York: Wiley.
  • Hall, P. 1981. Asymptotic theory of triple sampling for sequential estimation of a mean. The Annals of Statistics 9 (6):1229–38. doi:10.1214/aos/1176345639.
  • Isogai, E., and A. Futschik. 2010. Sequential estimation of a linear function of location parameters of two negative exponential distributions. Journal of Statistical Planning and Inference 140 (9):2416–24. doi:10.1016/j.jspi.2010.02.008.
  • Isogai, E., and C. Uno. 2018. Three-stage confidence intervals for a linear combination of locations of two negative exponential distributions. Metrika 81 (1):85–103. doi:10.1007/s00184-017-0635-y.
  • Johnson, N. L., S. Kotz, and N. Balakrishnan. 1995. Continuous univariate distributions, vol. 2. New York: Wiley.
  • Krishnamoorthy, K.,. S. Mukherjee, and H. Guo. 2007. Inference on reliability in two-parameter exponential stress–strength model. Metrika 65 (3):261–73. doi:10.1007/s00184-006-0074-7.
  • Krishnamoorthy, K., and Y. Xia. 2018. Confidence intervals for a two-parameter exponential distribution: One- and two-sample problems. Communications in Statistics - Theory and Methods 47 (4):935–52. doi:10.1080/03610926.2017.1313983.
  • Kumar, S., and H. I. Patel. 1971. A test for the comparison of two exponential distributions. Technometrics 13 (1):183–89. doi:10.2307/1267085.
  • Lawless, J. F. 2003. Statistical models and methods for lifetime data. 2nd ed. New York: Wiley.
  • Meeker, W. Q., and L. Escobar. 1998. Statistical methods for reliability data. New York: John Wiley & Sons.
  • Merrington, M., and C. Thompson. 1943. Tables of percentage points of the inverted beta (F) distribution. Biometrika 33 (1):73–88. doi:10.2307/2333621.
  • Mukhopadhyay, N. 1974. Sequential estimation of location parameter in exponential distributions. Calcutta Statistical Association Bulletin 23 (1–4):85–95. doi:10.1177/0008068319740105.
  • Mukhopadhyay, N. 1982. On the asymptotic regret while estimating the location of an exponential distribution. Calcutta Statistical Association Bulletin 31 (3–4):207–13. doi:10.1177/0008068319820310.
  • Mukhopadhyay, N. 1988. Sequential estimation problems for negative exponential populations. Communications in Statistics - Theory and Methods 17 (8):2471–506. doi:10.1080/03610928808829758.
  • Mukhopadhyay, N. 1990. Some Properties of a three-stage procedure with applications in sequential analysis. Sankhya, Series A 51:218–31.
  • Mukhopadhyay, N. 2000. Probability and statistical inference. New York: Marcel Dekker.
  • Mukhopadhyay, N., and S. R. Bapat. 2016a. Multistage point estimation methodologies for a negative exponential location under a modified linex loss function: Illustrations with infant mortality and bone marrow data. Sequential Analysis 35 (2):175–206. doi:10.1080/07474946.2016.1165532.
  • Mukhopadhyay, N., and S. R. Bapat. 2016b. Multistage estimation of the difference of locations of two negative exponential populations under a modified linex loss function: Real data illustrations from cancer studies and reliability analysis. Sequential Analysis 35 (3):387–412. doi:10.1080/07474946.2016.1206386.
  • Mukhopadhyay, N., and S. Darmanto. 1988. Sequential estimation of the difference of means of two negative exponential populations. Sequential Analysis 7 (2):165–90. doi:10.1080/07474948808836149.
  • Mukhopadhyay, N., and B. M. de Silva. 2009. Sequential methods and their applications. Boca Raton: CRC.
  • Mukhopadhyay, N., and H. I. Hamdy. 1984. On estimating the difference of location parameters of two negative exponential distributions. Canadian Journal of Statistics 12 (1):67–76. doi:10.2307/3314725.
  • Mukhopadhyay, N., and A. Mauromoustakos. 1987. Three-stage estimation procedures for the negative exponential distributions. Metrika 34 (1):83–93. doi:10.1007/BF02613132.
  • Mukhopadhyay, N., and A. R. Padmanabhan. 1993. A note on three-stage confidence intervals for the difference of locations: The exponential case. Metrika 40 (1):121–28. doi:10.1007/BF02613670.
  • 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. doi:10.1080/07474946.2016.1238264.
  • Mukhopadhyay, N., and Y. Zhuang. 2019. Two-sample two-stage and purely sequential methodologies for tests of hypotheses with applications: Comparing normal means when the two variances are unknown and unequal. Sequential Analysis 38 (1):69–115. doi:10.1080/07474946.2019.1574445.
  • Ranganathan, J., and B. Kale. 1979. Tests of hypotheses for reliability functions in two-parameter exponential models. Canadian Journal of Statistics 7 (2):177–84. doi:10.2307/3315117.
  • Shanker, R., H. Fesshaye, and S. Selvaraj. 2016. On modeling of lifetime data using one parameter akash, lindley and exponential distributions. Biometrics and Biostatistics International Journal 2:1–10.
  • Swanepoel, J. W. H., and J. W. J. van Wyk. 1982. Fixed width confidence intervals for the location parameter of an exponential distribution. Communications in Statistics - Theory and Methods 11 (11):1279–89. doi:10.1080/03610928208828311.
  • Son, M. S., L. D. Haugh, H. I. Hamdy, and M. C. Costanza. 1997. Controlling type II error while constructing triple sampling fixed precision confidence intervals for the normal mean. Annals of the Institute of Statistical Mathematics 49 (4):681–92. doi:10.1023/A:1003266326065.
  • Woodroofe, M. 1977. Second order approximation for sequential point and interval estimation. Annals of Statistics 5:984–95.
  • Yata, K. 2008. Two-stage equivalence tests that control both size and power. Sequential Analysis 27 (2):185–200. doi:10.1080/07474940801989178.

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