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Journals / Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics / 2019 / Cilt: 68 - Sayı: 1

A Generalized Version of Foster and Stuart's d-statistic

Halil TANIL
Pages
98–110
Publication Date
2019-02-01
DOI
—
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AI Summary & Key Takeaways

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

Also, a comparison between the proposed test and some well-known distribution-free tests is made in terms of empirical powers.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:Assume that only the lists of upper k-records and lower k-records of a finite sequence are available and the existence of a monotonic trend in location is interested in.
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Key Findings & Data:In this study, a distribution-free test based on the difference between the numbers of upper and lower k-records is proposed for this situation.
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Conclusion & Impact:Also, a comparison between the proposed test and some well-known distribution-free tests is made in terms of empirical powers.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Monotonic trend in location · kth-records · Top-k-lists

Abstract

Assume that only the lists of upper k-records and lower k-records of a finite sequence are available and the existence of a monotonic trend in location is interested in. In this study, a distribution-free test based on the difference between the numbers of upper and lower k-records is proposed for this situation. The exact and asymptotic distributions of the proposed test statistic are obtained for a random continuous sequence which is independent and identically distributed (i.i.d.). Also, a comparison between the proposed test and some well-known distribution-free tests is made in terms of empirical powers.

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Cite This Article

TANIL, H. (2019). A Generalized Version of Foster and Stuart's d-statistic. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, Cilt: 68 - Sayı: 1, 98–110. https://ajindex.com/articles/747026

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References (15)

  1. Ahsanullah, M. (2004). Record Values-Theory and Applications. Universiy Press of America, Lanham, MD. Aiyer, R. J., Guilliter, C. L. and Albers, W. (1979). Asymptotic relative efficiencies of rank tests for trend alternatives. Journal of American Statistical Association. 74, 226-231.
  2. Arnold, B.C., Balakrishnan, N. and Nagaraja, H.N. (1998).
  3. Records. John Wiley, New York. Chandler, K.N. (1952). The distribution and frequency of record values. Journal of the Royal Statistical Society, Series B. 14, 220-228.
  4. Cox, D.R. and Stuart, A. (1955). Some quick sign tests for trend in location and dispersion. Biometrika 42, 80-95.
  5. Daniels, H.E., (1950). Rank correlation and population models. Journal of Royal Statistical Society Series B. 12, 171-181.
  6. Diersen, J. and Trenkler, G. (1996). Records Tests for Trend in Location. Statistics. 28, 1-12.
  7. Dziubdziela, W. and Kopocinski, B. (1976). Limiting properties of the k-th record values. Appl. Math. 15, 187-190.
  8. 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.
  9. Hofmann, G. and Balakrishnan, N. (2006). A nonparametric test for trend based on initial ranks. Journal of Statistical Computation and Simulation. 76, 829-837.
  10. Kamps, U. (1995). A Concept of Generalized Order Statistics. Stuttgart: Teubner. Khraibani, Z., Jacob, C., Ducrot, C., Charras-Garrido, M. and Sala C. (2015). A non parametric exact test based on the number of records for an early detection of emerging events: Illustration in epidemiology. Communications in Statistics-Theory and Methods. 44, 726-749.
  11. Kozan, A. and Tanil, H. (2013). Bottom-k-Lists. İstatistik: Journal of the Turkish Statistical Association. 6, 73-79. López-Blázquez, F. and Wesołowski, J. (2007). Top-k-lists. Metrika. 65, 69--82. Mann, H. B. (1945). Nonparametric test against trend. Econometrica. 13, 245-259.
  12. Moore, G. H. and Wallis, W. A. (1943). Time series significance tests based on signs of differences. J. Amer. Statist. Ass. 38, 153-164.
  13. Nevzorov, V. (1988). Records. Theor. Prob. Appl. 32, 201-228.
  14. Nevzorov, V. (2000). Records: Mathematical Theory. Translation Mathematical Monographs Volume 194, American Mathematical Society, Province, RI 02940, USA. Razmkhah, M. and Ahmadi, J. (2013). Pitman closeness of current k-records to population quantiles. Statistics & Probability Letters. 83, 148-156.
  15. Redner, S. and Petersen, M. R. (2006). Role of global warm