RUNS BASED ON DISCRETE ORDER STATISTICS

Abstract

In the present paper, we study runs based on discrete order statistics. Limit results for the total number of such runs and the length of the longest run are derived.

Keywords

• Runs,order statistics,limit laws

References

1. Balakrishnan, N. and Koutras, M.V., (2002), Runs and scans with applications, Wiley Series in Probability and Statistics.
2. Brands, J.J.A.M., Steutel, F.W. and Wilms, R.J.G., (1994), On the number of maxima in a discrete sample, Statistics & Probability Letters, 20, 209–217.
3. Eisenberg, B., Stengle, G. and Strang, G., (1993), The asymptotic probability of a tie for first place, Annals of Applied Probability, 3, 731–745.
4. Eryilmaz, S., (2005), On the distribution and expectation of success runs in nonhomogeneous Markov dependent trials, Statistical Papers, 46(1), 117–128.
5. Eryilmaz, S., (2007), Extension of runs to the continuous valued sequences, Statistics & Probability Letters, 77(4), 383–388.
6. Eryilmaz, S., (2008), Distribution of runs in a sequence of exchangeable multi-state trials, Statistics & Probability Letters, 78, 1505–1513.
7. Eryilmaz, S. and Fu, J., (2008), Runs in continuous-valued sequences, Statistics & Probability Letters, 78, 759-765.
8. Eryilmaz, S. and Stepanov, A., (2008), Runs in an ordered sequence of random variables, Metrika, 67, 299–313. [9]Fan, A. H., Wang, Z. Z. and Ding, F. Q., (2008), Some limit theorems of runs to the continuousvalued sequence, Kybernetes, 37, 1279-1286.

9. Fu, J.C. and Lou W.Y.W., (2003), Distribution theory of runs and patterns and its applications, World Scientific Publishing, Singapore.
10. Stepanov, A., (2011a), Limit theorems for runs based on ’small’ spacings, Statistics & Probability Letters, 81, 54–61.
11. Stepanov, A., (2011b), Runs based on the ratios of consecutive order statistics, Communications in Statistics -Theory and Methods, 40(18), 3252–3268.
12. Alexei Stepanov is presently an Associate Professor at the Department of Mathematics of Izmir University of Economics, Turkey. He graduated from the Faculty of Mathematics and Mechanics of St.Petersburg (Leningrad)