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Bottom-k-Lists

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

Agah Kozan Halil Tanil

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

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 This is me

Halil Tanil

Publication Date July 1, 2013
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.
AMA Kozan A, Tanil H. Bottom-k-Lists. IJTSA. July 2013;6(2):73-79.
Chicago Kozan, Agah, and Halil Tanil. “Bottom-k-Lists”. Istatistik Journal of The Turkish Statistical Association 6, no. 2 (July 2013): 73-79.
EndNote Kozan A, Tanil H (July 1, 2013) Bottom-k-Lists. Istatistik Journal of The Turkish Statistical Association 6 2 73–79.
IEEE A. Kozan and H. Tanil, “Bottom-k-Lists”, IJTSA, vol. 6, no. 2, pp. 73–79, 2013.
ISNAD Kozan, Agah - Tanil, Halil. “Bottom-k-Lists”. Istatistik Journal of The Turkish Statistical Association 6/2 (July2013), 73-79.
JAMA 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, 2013, pp. 73-79.
Vancouver Kozan A, Tanil H. Bottom-k-Lists. IJTSA. 2013;6(2):73-9.