SavedAdd your journal

Journals / Süleyman Demirel Üniversitesi Fen Bilimleri Enstitüsü Dergisi / 2017 / Cilt: 21 - Sayı: 3

On Distributional Properties of Record Ranges and Record Range Times

Agah KOZAN
HALİL TANIL
Pages
843–846
DOI
—
🏛️Bibliographic metadata and full text access for this article are provided via DergiPark.
DergiPark Record ↗
✨

AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

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.

📌 3 Key Takeaways

🎯
Objective & Hypothesis: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.
📊
Key Findings & Data:The probability of changing the th record range by a new observation is also given.
💡
Conclusion & Impact: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.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Record range · record range times · record coverage

Özet

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.

🔖

Cite This Article

KOZAN, A., TANIL, H. (2017). On Distributional Properties of Record Ranges and Record Range Times. Süleyman Demirel Üniversitesi Fen Bilimleri Enstitüsü Dergisi, Cilt: 21 - Sayı: 3, 843–846. https://ajindex.com/articles/310208

📄 Full Text PDF Viewer

📄

PDF görüntüleyici hazırlanıyor...

References (20)

  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