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Cut-Off Points for Various Tests for Circular Uniformity

V. J. Devaraaj*, S. V. S. Girija**, A. V. Dattatreya Rao***

* Associate Professor, Department of Basic Science & Humanities, V.K.R, V.N.B and A.G.K. College of Engineering, Gudivada, (A.P), India.

** Associate Professor, Department of Mathematics, Hindu College, Guntur, (A.P), India.

*** Former Professor, Department of Statistics, Acharya Nagarjuna University, Guntur, (A.P), India.

Periodicity:October - December'2017
DOI : https://doi.org/10.26634/jmat.6.4.13863

Abstract

Because of central role played by Circular Uniform Distribution, the most important hypothesis about a distribution on the Circle is that of Uniformity. Though several tests were proposed, cut-off points for various sample sizes and level of significance were not made available in the literature. Hence, an attempt is made here to present tables of cut-off points and their utility in discussing goodness of fit of a model is presented.

Keywords

Circular Model, Cut-off Points, Goodness of Fit, Wrapped Lognormal, Wrapped Logistic, Wrapped Extreme-Value Models

How to Cite this Article?

Devaraaj, V.J., Girija, S.V.S., Rao, A.V.D. (2017). Cut-Off Points for Various Tests for Circular Uniformity. i-manager’s Journal on Mathematics, 6(4), 29-38. https://doi.org/10.26634/jmat.6.4.13863

References

[1]. Ajne, B. (1968). A simple test for uniformity of a circular distribution. Biometrika, 55(2), 343-354.

[2]. Cordeiro, G. M. Paula, G. A. & Botter, D. A. (1994). Improved likelihood ratio tests for dispersion models. Internat. Statist. Rew., 62(2), 257-274.

[3]. Cox, D. R. & Hinkley, D. V. (1974). Theoretical Statistics. Chapman & Hall.

[4]. Fernandez-Duran, J. J. & Gregorio-Dominguez, M. M. (2010). A Likelihood Ratio Test for Homogeneity in Circular Data. J Biomet Biostat., 1, 107.

[5]. Fisher, N. I. (1993). Statistical Analysis of Circular Data. Cambridge University Press, Cambridge.

[6]. Fisher, N. I. & Powell, C. M. (1989). Statistical analysis of two-dimensional palaeocurrent data: methods and examples. Journal of the Geological Society of Australia, 36(1), 91-107.

[7]. Hodges J. L. (1955). A bivariate sign test. Ann. Math. Statis., 26(3), 523-527.

[8]. Kuiper, N. H. (1960). Tests conccrning random points on a circle. Ned. Akad. Wet.Pmc. Ser. A, 63, 38-47.

[9]. Laubscher, N. F. & Rudolpli, G. J. (1968). A distribution arising from random points on the circumference of a circle. Res. Report No 268. C.S.I. R., Pretoria. [189, 310].

[10]. Mardia, K. V. & Jupp, P. (2000). Directional Statistics. John Wiley, Hoboken, NJ.

[11]. Marrero, O. (1983). The performance of several statistical tests for seasonality in monthly data. Journal of Statistical Computation and Simulation, 17(4), 275-296.

[12]. Rao J. S. & Sen Gupta, A. (2001). Topics in Circular Statistics,.World Scientific Press, Singapore.

[13]. Rao, J. S. (1969). Some contributions to the analysis of circular data (Doctoral Dissertation, Indian Statistical Institute, Kolkata).

[14]. Stephens, M. A. (1970). Use of the Kolmogorov-Smirnov, Cramér-Von Mises and related statistics without extensive tables. Journal of the Royal Statistical Society. Series B (Methodological), 115-122.

[15]. Watson, G. S. (1961). Goodness-of-fit tests on a circle. Biometrika, 48(½), 109-114.

[16]. Watson, G. S. (1962). Goodness-of-fit tests on a circle. II. Biometrika, 49(½), 57-63.

[17]. Watson, G. S. (1967). Another test for the uniformity of a circular distribution. Biometrika, 54(3-4), 675-677. Appendix

Cut-Off Points for Various Tests for Circular Uniformity

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