Journals / Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics / 2026 / Volume: 69 Issue: 1

Confidence regions for bivariate probability density functions using polygonal areas

Orhan Kesemen(Karadeniz Technical University)0000-0002-5160-1178
Eda Özkul(Karadeniz Technical University)0000-0002-9840-8818
Ülkü Ünsal(Karadeniz Technical University)0000-0002-8363-1806
Pages
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Publication Date
2020-06-30
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In this study, a polygonal approach is suggested to generalize the

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Objective & Hypothesis:In this study, a polygonal approach is suggested to generalize the
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Key Findings & Data:In this study, a polygonal approach is suggested to generalize the
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Conclusion & Impact:In this study, a polygonal approach is suggested to generalize the
🔬Design:Research Article
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⚙️Variables:bivariate probability density functions · Bivariate confidence region · multimodal confidence region

Abstract

In this study, a polygonal approach is suggested to generalize the

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Cite This Article

Kesemen, O., Özkul, E., Ünsal, Ü. (2020). Confidence regions for bivariate probability density functions using polygonal areas. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, Volume: 69 Issue: 1. https://doi.org/10.31801/cfsuasmas.542499

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References (22)

  1. Neyman, J., Outline of a theory of statistical estimation based on the classical theory of probability, Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences 236(767), (1937), 333--380.
  2. Tate, R. F., and Klett, G. W., Optimal confidence intervals for the variance of a normal distribution, Journal of the American statistical Association 54(287), (1959), 674--682.
  3. Dunn, O., Multiple comparisons among means, Journal of the American Statistical Association 56(293), (1961), 52--64.
  4. Dunn, O., Multiple comparisons using rank sums, Technometrics 6(3), (1964), 241--252.
  5. Chew, V., Confidence, prediction, and tolerance regions for the multivariate normal distribution, Journal of the American Statistical Association 61(315), (1966), 605--617.
  6. Sidak, Z., Rectangular confidence regions for the means of multivariate normal distributions, Journal of the American Statistical Association 62(318), (1967), 626--633.
  7. Hu, Z., and Yang, R.-C., A new distribution-free approach to constructing the confidence region for multiple parameters, PloS one 8(12), (2013), e81179.
  8. Mammen, E., and Polonik, W., Confidence regions for level sets, Journal of Multivariate Analysis 122, (2013), 202--214.
  9. Martin, R., Random sets and exact confidence regions, Sankhya A 76(2), (2014), 288--304.
  10. Rambaud-Althaus, C., Althaus, F., Genton, B., and D'Acremont, V., Clinical features for diagnosis of pneumonia in children younger than 5 years: a systematic review and meta-analysis, The Lancet Infectious Diseases 15(4), (2015), 439--450.
  11. Harrar, S., and Xu, J., Confidence regions for level differences in growth curve models, Journal of Statistical Planning and Inference 175, (2016), 11--24.
  12. Öztürk, F., and Karabulut, İ.,Interval Estimators for the Parameters of the Normal Distribution, Commun.Fac.Sci.Univ.Ank.Series A1 55(1), (2006), 23--32.
  13. Ünsal, Ü., Determining Polygonal Confidence Zone with Artificial Bee Colony Algorithm and an Application in Mines, MSc Thesis, Karadeniz Technical University, Turkey, 2014.
  14. Kesemen O., Tiryaki, B. K., Özkul, E. and Tezel, Ö., Determination of the Confidence Intervals for Multimodal Probability Density Functions, Gazi University Journal of Science 31(1), (2018) 310--326.
  15. Kesemen O., Tiryaki, B. K. and Uluyurt, T., A Novel Approximation for Computation Bivariate Distribution Functions in Polygonal Area, Gümüşhane Üniversitesi Fen Bilimleri Enstitüsü Dergisi 9(1), (2019) 88--98.
  16. Douglas, D., and Peucker, T., Algorithms for the reduction of the number of points required to represent a digitized line or its caricature, Cartographica: The International Journal for Geographic Information and Geovisualization 10(2), (1973), 112--122.
  17. Kesemen O. and Tiryaki, B. K., Non-Uniform Random Number Generation from Arbitrary Bivariate Distribution in Polygonal Area, Süleyman Demirel Üniversitesi Fen Bilimleri Enstitüsü Dergisi 22(2), (2018), 443--457.
  18. Chew, L., Constrained delaunay triangulations, Algorithmica 4(1-4), (1989), 97--108.
  19. Thacker, W. C., A brief review of techniques for generating irregular computational grids, International Journal for Numerical Methods in Engineering 15(9), (1980), 1335-1341.
  20. Fulton, S. R., Ciesielski, P. E., and Schubert, W. H., Multigrid methods for elliptic problems: A review. Monthly Weather Review 114 (5), (1986), 943-959.
  21. Sulman, M., Williams, J. F., and Russell, R. D., Optimal mass transport for higher dimensional adaptive grid generation, Journal of computational physics 230(9), (2011), 3302-3330.
  22. Stilitz, I., and Yitzhaky, J., The effect of grid size on street location time in maps, Applied ergonomics 10(4), (1979), 235-239. Özmen, B., Nurlu, M., and Güler, H., Coğrafi Bilgi Sistemi ile Deprem Bölgelerinin İncelenmesi, Bayındırlık ve İskan Bakanlığı, Afet İşleri Genel Müdürlüğü, Ankara, 1997.