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Bottom-k-Lists

Year 2013, Volume: 6 Issue: 2, 73 - 79, 01.07.2013

Agah Kozan , Halil Tanil

https://izlik.org/JA33MX58MA

Abstract

Consider an infinite sequence of iid continuous random variables. In this paper, we introduce duals of top-k-lists which is called ”Bottom-k-lists”. We also derive the joint probability density function (pdf) of the ordered elements of `th bottom-k-list and its relation with the joint pdf of dual (lower) generalized order statistics (dGOS). In addition, we give a distributional relation between each element of l-th bottom-k-list, ordinary order statistics (oOS), and lower k-records.

Keywords

Lower k-records Bottom-k-lists Dual generalized order statistics Meijer’s G function Ordinary order statistics

References

  • Burkschat,M., Cramer. E., Kamps, U., 2003. Dual generalized order statistics. METRON - International Journal of Statistics vol. LXI, n. 1, 13-26.
  • Burkschat,M., Lenz, B., 2009.Marginal distributions of the counting process associated with generalized order statistics. Communications in Statistics-Theory and Methods 38, 2089-2106.
  • Erdelyi, A., Magnus,W., Oberhettinger, F. and Tricomi, F., G., 1953. Higher Transcendental Functions, McGraw-Hill, New York.
  • L´opez-Bl´azques, F., Weso lowski, J., 2007. Top-k-lists. Metrika 65, 69-82.
  • Luke, Y., L., 1969. The Special Functions and Their Approximations, Academic Press, New York.
  • Mathai, A., M., 1993. A Handbook of Generalized Special Functions for Statistical and Physical Sciences, Clarendon Press, Oxford.
  • Mathai, A., M. and Haubold, H. J., 2008. Special Functions for Applied Scientists, Springer, New York.
  • Pawlas, P., Szynal, D., 1998. Relations for single and product moments of k-th record values from exponential and Gumbel distributions, J. Appl. Statist. Sci. 7, 53-61.
  • Pawlas, P., Szynal, D., 2001. Recurrence relations for single and product moments of lower generalized order statistics from the inverse Weibull distribution, Demonstratio Mathematica 34(2), 353-358.
  • Tanil, H., 2009. An order statistics model based on the list of top m scores after `th change, J. Statist. Plann. Infer., 139, 2189-2195.

Year 2013, Volume: 6 Issue: 2, 73 - 79, 01.07.2013

Agah Kozan , Halil Tanil

https://izlik.org/JA33MX58MA

Abstract

References

  • Burkschat,M., Cramer. E., Kamps, U., 2003. Dual generalized order statistics. METRON - International Journal of Statistics vol. LXI, n. 1, 13-26.
  • Burkschat,M., Lenz, B., 2009.Marginal distributions of the counting process associated with generalized order statistics. Communications in Statistics-Theory and Methods 38, 2089-2106.
  • Erdelyi, A., Magnus,W., Oberhettinger, F. and Tricomi, F., G., 1953. Higher Transcendental Functions, McGraw-Hill, New York.
  • L´opez-Bl´azques, F., Weso lowski, J., 2007. Top-k-lists. Metrika 65, 69-82.
  • Luke, Y., L., 1969. The Special Functions and Their Approximations, Academic Press, New York.
  • Mathai, A., M., 1993. A Handbook of Generalized Special Functions for Statistical and Physical Sciences, Clarendon Press, Oxford.
  • Mathai, A., M. and Haubold, H. J., 2008. Special Functions for Applied Scientists, Springer, New York.
  • Pawlas, P., Szynal, D., 1998. Relations for single and product moments of k-th record values from exponential and Gumbel distributions, J. Appl. Statist. Sci. 7, 53-61.
  • Pawlas, P., Szynal, D., 2001. Recurrence relations for single and product moments of lower generalized order statistics from the inverse Weibull distribution, Demonstratio Mathematica 34(2), 353-358.
  • Tanil, H., 2009. An order statistics model based on the list of top m scores after `th change, J. Statist. Plann. Infer., 139, 2189-2195.
There are 10 citations in total.

Details

Primary Language English
Journal Section Research Article
Authors

Agah Kozan

Halil Tanil

Publication Date July 1, 2013
IZ https://izlik.org/JA33MX58MA
Published in Issue Year 2013 Volume: 6 Issue: 2

Cite

APA Kozan, A., & Tanil, H. (2013). Bottom-k-Lists. Istatistik Journal of The Turkish Statistical Association, 6(2), 73-79. https://izlik.org/JA33MX58MA
AMA 1.Kozan A, Tanil H. Bottom-k-Lists. IJTSA. 2013;6(2):73-79. https://izlik.org/JA33MX58MA
Chicago Kozan, Agah, and Halil Tanil. 2013. “Bottom-k-Lists”. Istatistik Journal of The Turkish Statistical Association 6 (2): 73-79. https://izlik.org/JA33MX58MA.
EndNote Kozan A, Tanil H (July 1, 2013) Bottom-k-Lists. Istatistik Journal of The Turkish Statistical Association 6 2 73–79.
IEEE [1]A. Kozan and H. Tanil, “Bottom-k-Lists”, IJTSA, vol. 6, no. 2, pp. 73–79, July 2013, [Online]. Available: https://izlik.org/JA33MX58MA
ISNAD Kozan, Agah - Tanil, Halil. “Bottom-k-Lists”. Istatistik Journal of The Turkish Statistical Association 6/2 (July 1, 2013): 73-79. https://izlik.org/JA33MX58MA.
JAMA 1.Kozan A, Tanil H. Bottom-k-Lists. IJTSA. 2013;6:73–79.
MLA Kozan, Agah, and Halil Tanil. “Bottom-k-Lists”. Istatistik Journal of The Turkish Statistical Association, vol. 6, no. 2, July 2013, pp. 73-79, https://izlik.org/JA33MX58MA.
Vancouver 1.Agah Kozan, Halil Tanil. Bottom-k-Lists. IJTSA [Internet]. 2013 Jul. 1;6(2):73-9. Available from: https://izlik.org/JA33MX58MA