New Circular model induced by Inverse Stereographic projection on Double Exponential Model - Application to Birds Migration Data

Girija, S.V.S.; Rao, A.V. Dattatreya; Yedlapalli, Phani

doi:10.2478/jamsi-2014-0001

Abstract

This paper introduces Stereographic Double Exponential Model based on inverse Stereographic Projection or Bilinear (Mobius) Transformation, [Minh and Farnum (2003)]. onsidering the data set of 13 homing pigeons were released singly in the Toggenburg Valley in Switzerland under sub Alpine conditions (data quoted in Batschelet (1981)), it is shown that the said model is a good fit by most of the tests at various level of significance. The derivation of the characteristic function for Stereographic Double Exponential Model and its trigonometric moments are presented. Relative performance of Stereographic Logistic [Phani (2013], Wrapped Logistic [Dattatreya Rao et al (2007)] and Stereographic Double Exponential models for the live data of 13 birds is studied. Also graphs of pdf of this new Model for various combinations of the parameters are drawn.

References

1. Abramowitz, M. Stegun, I.A. (1965), Handbook of Mathematical Functions, Dover, New York.
Search in Google Scholar
2. Dattatreya Rao, A.V., Ramabhadra Sarma, I. and Girija, S.V.S. (2007), On Wrapped Version of Some Life Testing Models, Comm Statist,- Theor. Meth., 36, issue # 11, pp.2027-2035.
Search in Google Scholar
3. Dattatreya Rao, A.V., Girija, S.V.S., Phani. Y. (2011), Differential Approach to Cardioid Distribution, Computer Engineering and Intelligent Systems, Vol 2, No.8, pp. 1-6.
Search in Google Scholar
4. Devaraaj V. J. (2012), Some Contributions to Circular Statistics, Thesis submitted to Acharya Nagarjuna University for the award of Ph. D.
Search in Google Scholar
5. Girija, S.V.S., (2010), Construction of New Circular Models, VDM - VERLAG, Germany.
Search in Google Scholar
6. Gradshteyn and Ryzhik (2007). Table of Integrals, series and products, 7th edition, Academic Press.
Search in Google Scholar
7. Jammalamadaka S. Rao and Sen Gupta, A. (2001), Topics in Circular Statistics, World Scientific Press, Singapore.10.1142/4031
Search in Google Scholar
8. Lukacs, E. and Laha, R.G. (1970), Applications of Characteristic Functions, Charles Griffin and Company Limited, London, second edition.
Search in Google Scholar
9. Mardia, K.V. and Jupp, P.E. (2000), Directional Statistics, John Wiley, Chichester.10.1002/9780470316979
Search in Google Scholar
10. Minh, Do Le and Farnum, Nicholas R. (2003), Using Bilinear Transformations to Induce Probability Distributions, Communication in Statistics - Theory and Methods, 32, 1, pp. 1 - 9.
Search in Google Scholar
11. Phani Y. (2013), On Stereographic Circular and Semicircular Models, Thesis submitted to Acharya Nagarjuna University for the award of Ph.D.
Search in Google Scholar
12. Ramabhadrasarma, I. A.V. Dattatreya Rao and S.V.S. Girija (2009), On Characteristic Functions of Wrapped Half Logistic and Binormal Distributions, International Journal of Statistics and Systems, Volume 4 Number 1, pp. 33-45.
Search in Google Scholar
13. Ramabhadrasarma, I. A.V. Dattatreya Rao and S.V.S. Girija (2011), On Characteristic Functions of Wrapped Lognormal and Weibull Distributions, Journal of Statistical Computation and Simulation, Vol. 81, No. 5, 579-589.
Search in Google Scholar
14. Toshihiro Abe, Kunio Shimizu and Arthur Pewsey, (2010), Symmetric Unimodal Models for Directional Data Motivated by Inverse Stereographic Projection, J. Japan Statist. Soc., Vol. 40 (No. 1), pp. 45-61.10.14490/jjss.40.045
Search in Google Scholar

New Circular model induced by Inverse Stereographic projection on Double Exponential Model - Application to Birds Migration Data

Abstract

Paradigm

My account