On Distributional Properties of Record Ranges and Record Range Times

Year 2017, , 843 - 846, 13.10.2017

Halil Tanıl , Agah Kozan

https://doi.org/10.19113/sdufbed.18244

Abstract

In this paper, some distributional results concerning the number of record ranges in the first  independent and identically distributed (iid) continuous random observations are obtained. The probability of changing the th record range by a new observation is also given. Furthermore, we introduce the times of record ranges and derive their joint probability mass function. One of the main results found in this paper is that record range times have finite expected values although usual record times have infinite expected values.

Keywords

Record range, record range times, record coverage, current record, extreme value

References

• [1] Chandler, K.N., 1952. The distribution and frequency of record values. Journal of the Royal Statistical Society, Series B, 14, 220-228.
• [2] Foster, F.G. and Stuart, A., 1954. Distribution-free tests in time-series based on the breaking of records (with discussions). Journal of the Royal Statistical Society, Series B., 16, 2-22.
• [3] Shorrock, R.W., 1972. On record values and record times. Journal of Applied Probability, 9, 316-326.
• [4] Resnick, S.I., 1973. Record values and Maxima. The Annals of Probability, 1(4), 650-662.
• [5] Galambos, J., 1978. The Asymptotic Theory of Extreme Order Statistics. John Wiley, New York.
• [6] Glick, N., 1978. Breaking records and breaking boards. American Mathematical Monthly, 85, 2-26.
• [7] Dunsmore, I.R., 1983. The future occurence of records. Annals of the Institude of Statistical Mathematics, 35, 267-277.
• [8] Nagaraja, H.N., 1988. Record Values and Related Statistics. A review, Communication in Statistics, Theory and Methods, 17, 2223-2238.
• [9] Nevzorov, V., 1988. Records. Theor. Prob. Appl. 32, 201-228.
• [10] Ahsanullah, M., 1995. Record Statistics. Nova Science Publishers Inc. Commack. NY.
• [11] Borovkov, K., Pfeifer, D., 1995. On record indices and record times. Journal of Statistical Planning and Inference, 45, 65-80.
• [12] Feuerverger, A., Hall, P., 1998. On statistical inference based on record values. Extremes. 1(2), 169-190.
• [13] Arnold, B.C., Balakrishnan, N. and Nagaraja, H.N., 1998. Records. John Wiley. New York.
• [14] Houchens, R.L., 1984. Record value, theory and inference. Ph.D. Dissertation, University of California, Riverside.
• [15] Basak, P., 2000. An application of record range and some characterization results. In: Balakrishnan, N. (eds.) Advances on Theoretical and Methodological Aspects of Probability and Statistics, pp. 83-95. Newark, NJ, Gordon and Breach.
• [16] Ahmadi, J., Balakrishnan, N., 2004. Confidence intervals for quantiles in terms of record range. Statistics and Probability Letters, 68, 395-405.
• [17] Ahmadi, J., Balakrishnan, N., 2005. Distribution-free confidence intervals for quantile intervals based on current records. Statistics and Probability Letters 75, 190-202.
• [18] Raqab, M.Z., 2007. Inequalities for expected current record statistics. Communication in Statistics, Theory and Methods, 36, 1367-1380.
• [19] Raqab, M.Z., 2009. Distribution-free prediction intervals for the future current record statistics. Stat Papers, 50, 429-439.
• [20] Ahmadi, J., Balakrishnan, N., 2011. Distribution-free prediction intervals for orders statistics based on record coverage. Journal of the Korean Statistical Society, 40, 181-192.
• [21] Tanil, H., 2009. An order statistics model based on the list of top m scores after ℓth change. Journal of Statistical Planning and Inference, 139, 2189-2195.
• [22] Bairamov, I.G., 1997. Some distribution free properties of statistics based on record values and characterizations of the distribution through a record. Journal of Applied Statistical Science. Sci, 5(1), 17-25.