140
Views
0
CrossRef citations to date
0
Altmetric
Article

Topp-Leone distribution with an application to binomial sampling

ORCID Icon &
Pages 4075-4086 | Received 02 Jan 2021, Accepted 30 Jun 2021, Published online: 09 Sep 2021

References

  • Banks, J. S., and R. K. Sundaram. 1992. Denumerable-armed bandits. Econometrica 60 (5):1071–96. doi:10.2307/2951539.
  • Barlow, R., and F. Proschan. 1975. Statistical theory of reliability and life testing: Probability models. New York: Holt-Rinehart and Winston.
  • Berry, D. A., R. W. Chen, A. Zame, D. C. Heath, and L. A. Shepp. 1997. Bandit problems with infinitely many arms. The Annals of Statistics 25 (5):2103–16. doi:10.1214/aos/1069362389.
  • Berry, D. A., and B. Fristedt. 1985. Bandit problems: Sequential allocations of experiments. London: Chapman and Hall.
  • Chen, K. Y., and C. T. Lin. 2004. A note on strategies for bandit problems with infinitely many arms. Metrika 59 (2):193–203. doi:10.1007/s001840300279.
  • Chen, K. Y., and C. T. Lin. 2005. A note on infinite-arm Bernoulli bandit problems with generalized beta prior distributions. Statistical Papers 46 (1):129–40. doi:10.1007/BF02762039.
  • Genç, A. İ. 2012. Moments of order statistics for Topp-Leone distribution. Statistical Papers 53 (1):117–31. doi:10.1007/s00362-010-0320-y.
  • Genç, A. İ. 2013. Estimation of P(X>Y) with Topp-Leone distribution. Journal of Statistical Computation and Simulation 53:117–31.
  • Ghitany, M. E. 2007. Asymptotic distribution of order statistics from the Topp-Leone distribution. International Journal of Applied Mathematics 20:371–6.
  • Ghitany, M. E., S. Kotz, and M. Xie. 2005. On some reliability measures and their stochastic orderings for the Topp-Leone distribution. Journal of Applied Statistics 32 (7):715–22. doi:10.1080/02664760500079613.
  • Gittins, J. C. 1989. Multi-armed bandit allocation indices. New York: John Wiley & Sons.
  • Gittins, J. C., K. Glazebrook, and R. Weber. 2011. Multi armed bandit allocation indices, 2nd ed. Hoboken, NJ: John Wiley & Sons.
  • Herschkorn, S. J., E. Pekoz, and S. M. Ross. 1996. Policies without memory for the infinite-armed Bernoulli bandit under the average-reward criterion. Probability in the Engineering and Informational Sciences 10 (1):21–8. doi:10.1017/S0269964800004149.
  • Kapur, K. C., and L. R. Lamberson. 1977. Reliability in engineering design. New York: John Wiley & Sons, Inc.
  • Kotz, S., and S. Nadarajah. 2006. J-shaped distribution, Topp and Leone’s. Encyclopedia of statistical sciences, vol. 6, 2nd ed., 3786. Hoboken, NJ: John Wiley & Sons.
  • Kotz, S., and J. R. Van Dorp. 2004. Beyond beta-other continuous families of distributions with bounded support and applications. Singapore: World Scientific.
  • Lin, C. T., and C. J. Shiau. 2000. Some optimal strategies for bandit problems with beta prior distributions. Annals of the Institute of Statistical Mathematics 52 (2):397–405. doi:10.1023/A:1004130209258.
  • Nadarajah, S., and S. Kotz. 2003. Moments of some J-shaped distributions. Journal of Applied Statistics 30 (3):311–7. doi:10.1080/0266476022000030084.
  • Pham, T. G., and Q. P. Duong. 1989. The generalized Beta- and F-distributions in statistical modelling. Mathematical and Computer Modelling 12 (12):1613–25. doi:10.1016/0895-7177(89)90337-3.
  • Robbins, H. 1952. Some aspects of the sequential design of experiments. Bulletin of the American Mathematical Society 58 (5):527–36. doi:10.1090/S0002-9904-1952-09620-8.
  • Topp, C. W., and F. C. Leone. 1955. A family of J-shaped frequency functions. Journal of the American Statistical Association 50 (269):209–19. doi:10.1080/01621459.1955.10501259.
  • Van Dorp, J. R., and S. Kotz. 2004. Modeling income distributions using elevated distributions on a bounded domain. Unpublished manuscript. The George Washington University, Washington, DC.
  • Vicari, D., J. R. Van Dorp, and S. Kotz. 2008. Two-sided generalized Topp and Leone (TS-GTL) distributions. Journal of Applied Statistics 35 (10):1115–29. doi:10.1080/02664760802230583.
  • Whittle, P. 1982. Optimization over time-1. New York: John Wiley & Sons.
  • Whittle, P. 1983. Optimization over time-2. New York: John Wiley & Sons.
  • Zhou, M., D. W. Yang, Y. Wang, and S. Nadarajah. 2006. Some j-shaped distributions: Sums, products and ratios. RAMS ’06. Annual Reliability and Maintainability Symposium, 175–81. doi:10.1109/RAMS.2006.1677371.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.