References
- M. Abramowitz and I. Stegun, Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, Applied Mathematics Series, vol. 55, National Bureau of Standards, 1972.
- S. Bhattacharya and A. SenGupta, Bayesian analysis of semiparametric linear-circular models, J. Agric. Biol. Environ. Stat. 14 (2009), pp. 33–65. doi: https://doi.org/10.1198/jabes.2009.0003
- D.R. Cox, Contribution to discussion of Mardia (1975a). Journal of Royal Statistical Society B. 37 (1975), pp. 380–381.
- J.J. Fernndez-Durn and M.M. Gregorio-Domiguez, Modeling angles in proteins and circular genomes using multivariate angular distributions based on multiple nonnegative trigonometric sums, Stat. Appl. Genet. Mol. Biol. 13 (2014), pp. 1–18. doi: https://doi.org/10.1515/sagmb-2012-0012
- N.I. Fisher, Statistical Analysis of Circular Data, Cambridge University Press, London, 1993.
- K. Horimoto, M. Suyama, H. Toh, K. Mori, and J. Otsuka, A method for comparing circular genomes from gene locations: application to mitochondrial genomes, Bioinformatics 14 (1998), pp. 789–802. doi: https://doi.org/10.1093/bioinformatics/14.9.789
- S. Jammalamadaka and A. SenGupta, Topics in Circular Statistics, World Scientific Inc., New York, 2001.
- A. Kagan, Y. Linnik, and C.R. Rao, Characterization Problems in Mathematical Statistics, Wiley and Sons Inc., New York, 1973.
- S. Kim and A. SenGupta, A three-parameter generalized von Mises distribution, Stat. Papers 54 (2012), pp. 685–693. doi: https://doi.org/10.1007/s00362-012-0454-1
- S. Kim and A. SenGupta, Multivariate-multiple circular regression, J. Stat. Comput. Simul. 87 (2017), pp. 1–15. doi: https://doi.org/10.1080/00949655.2016.1187608
- S. Kim, A. SenGupta, and B.C. Arnold, A multivariate circular distribution with applications to the protein structure prediction problem, J. Mutivariate Anal. 143 (2016), pp. 374–382. doi: https://doi.org/10.1016/j.jmva.2015.09.024
- D. Liu, S.D. Peddada, L. Li, and C.R. Weinberg, Phase analysis of circadian-related genes in two tissues, BMC. Bioinformatics. 7 (2006), pp. 87–96. doi: https://doi.org/10.1186/1471-2105-7-87
- K. Mardia, G. Hughes, C.C. Taylor, and H. Singh, A multivariate von Mises distribution with applications to bioinformatics, The Canadian J. Stat. 36 (2008), pp. 99–109. doi: https://doi.org/10.1002/cjs.5550360110
- K. Mardia and P. Jupp, Directional Statistics, Wiley and Sons Inc., New York, 1999.
- J. McKay, On computing discriminant, Am. Math. Mon. 94 (1987), pp. 523–527. doi: https://doi.org/10.1080/00029890.1987.12000677
- G.S. Shieh, S. Zheng, R.A. Johnson, Y. Chang, K. Shimizu, C. Wang, and S. Tang, Modeling and comparing the organization of circular genomes, Bioinformatics 27 (2011), pp. 912–918. doi: https://doi.org/10.1093/bioinformatics/btr049
- J.V. Uspensky, Theory of Equations, McGraw-Hill Inc., New York, 1963.
- R. von Mises, Uber die ganzzahligkeit der atomgewicht und verwandte fragen, Physikal 19 (1918), pp. 490–500.
- E.A. Yifantis and L.E. Borgman, An extension of the von Mises distribution, Commun. Stat.: Theory and Meth. 11 (1982), pp. 1695–1706. doi: https://doi.org/10.1080/03610928208828342