Research Article
Year 2013,
Volume: 6 Issue: 2, 73 - 79, 01.07.2013
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
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 | Articles |
| Authors | |
| Publication Date | July 1, 2013 |
| Published in Issue | Year 2013 Volume: 6 Issue: 2 |
