Inverse stereographic hyperbolic secant distribution: a new symmetric circular model by rotated bilinear transformations
The inverse stereographic projection (ISP), or equivalently, bilinear transformation, is a method to produce a circular distribution based on an existing linear model. By the genesis of the ISP method, many important circular models have been provided by many researchers. In this study, we propose a new symmetric unimodal/bimodal circular distribution by the rotated ISP method considering the hyperbolic secant distribution as a baseline distribution. Rotation means that fixing the origin and rotating all other points the same amount counterclockwise. Considering the effect of rotation on the circular distribution to be obtained with the bilinear transformation, it is seen that it actually induces a location parameter in the obtained circular probability distribution. We analyze some of the stochastic properties of the proposed distribution. The methods for the parameter estimation of the new circular model and the simulation-based compare results of these estimators are extensively provided by the paper. Furthermore, we compare the fitting performance of the new model according to its well-known symmetric alternatives, such as Von-Misses, and wrapped Cauchy distributions, on a real data set. From the information obtained by the analysis on the real data, we say that the fitting performance of the new distribution is better than its alternatives according to the criteria frequently used in the literature.
Keywords:
circular distribution, inverse stereographic, bilinear transformation, Mobius transformation rotation,
___
- Chaubey, Y. P., Karmaker, S. C., On some circular distributions induced by inverse stereographic projection, Sankhya B (2019), 1-23. https://dx.doi.org/https://doi.org/10.1007/s13571-019-00201-1.
- Dattatreya Rao, A., Girija, S., Phani, Y., Stereographic logistic model-application to noisy scrub birds data, Chilean Journal of Statistics, 7(2) (2016), 69-79.
- Fisher, N. I., Lewis, T., Embleton, B. J., Statistical Analysis of Spherical Data, Cambridge University Press, 1993.
- Girija, S., Rao, A., Yedlapalli, P., On stereographic lognormal distribution, International Journal of Advances in Applied Sciences, 2(3) (2013), 125-132.
- Girija, S., Rao, A. D., Yedlapalli, P., New circular model induced by inverse stereographic projection on double exponential model-application to birds migration data, Journal of Applied Mathematics, Statistics and Informatics, 10 (1) (2014), 5-17. https://dx.doi.org/https://doi.org/10.2478/jamsi-2014-0001.
- Kato, S., Jones, M., A family of distributions on the circle with links to, and applications arising from, Möbius transformation, Journal of the American Statistical Association, 105(489) (2010), 249-262. https://dx.doi.org/https://doi.org/10.1198/jasa.2009.tm08313.
- Mardia, K. V., Jupp, P. E., Directional Statistics, vol. 494, John Wiley & Sons, 2009.
- Minh, D. L., Farnum, N. R., Using bilinear transformations to induce probability distributions, Communications in Statistics-Theory and Methods, 32(1) (2003), 1-9. https://dx.doi.org/https://doi.org/10.1081/STA-120017796.
- Needham, T., Visual Complex Analysis, Oxford University Press, 1998.
- Swain, J. J., Venkatraman, S., Wilson, J. R., Least-squares estimation of distribution functions in johnson's translation system, Journal of Statistical Computation and Simulation, 29(4) (1988), 271-297. https://dx.doi.org/https://doi.org/10.1080/00949658808811068.
- Yedlapalli, P., Girija, S., Dattatreya Rao, A., Srihari, G., Symmetric circular model induced by inverse stereographic projection on double Weibull distribution with application, International Journal of Soft Computing, Mathematics and Control, 4 (2015), 69-76. https://dx.doi.org/https://doi.org/10.14810/ijscmc.2015.4106
- Yedlapalli, P., Sastry, K., Rao, A., On stereographic semicircular quasi lindley distribution, Journal of New Results in Science, 8 (2019), 6 -13.
- ISSN: 1303-5991
- Yayın Aralığı: Yılda 4 Sayı
- Başlangıç: 1948
- Yayıncı: Ankara Üniversitesi