i-manager Publications

The Semicircular Reflected Gamma Distribution

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

* Associate Professor, Department of Mathematics, Shri Vishnu Engineering College for Women, Bhimavaram, India.

** Associate Professor, Department of Mathematics, Hindu College, Guntur, India

*** Professor, Department of Statistics, Acharya Nagarjuna University, Guntur, India.

Periodicity:January - March'2016
DOI : https://doi.org/10.26634/JMAT.5.1.4870

Abstract

Modeling of circular data with limited number of available circular models such as, von Mises, Wrapped Cauchy, Cardioid, etc., was done in various domains like Neuro Science, Geography, Archaeology, Remote Sensing, Spatial Analysis, Plant Phenology and Political Science. Dattatreya Rao (2007; 2011a;2011b;2011c; 2013a; 2013b; 2016) and Girija (2010; 2013a; 2013b; 2014a; 2014b), Phani (2012a; 2012b; 2013a; 2013; 2014; 2015a; 2015b; 2015c; 2015d), Radhika (2013a; 2013b; 2014;2015) and Devaraaj (2012; 2014) have introduced several new models and a few new methodologies of constructing the new circular models. These circular models are constructed by applying wrapping method, inverse stereographic projection, offsetting and the rising sun function. It is observed that, the simple projection method is not a much paid attention in constructing circular models. Glancing the literature, semicircular, arc and skewed angular data were observed in the applications and sufficient number of models for such data is not available. Motivated by these points, the authors have introduced semicircular reflected gamma distribution for modelling semicircular data by a simple projection method on reflected gamma distribution. The authors have extend it to the laxial reflected gamma distribution by a simple projection for modeling any arc of arbitrary length, and also the first four trigonometric moments has been derived for the proposed model.

Keywords

Angular Data, Characteristic Function, Semicircular Model, Stereographic Double Exponential Distribution, Semicircular Laplace Distribution, Stereographic Projection, l-axial Data, Projection Trigonometric Moments.

How to Cite this Article?

Yedlapalli,P., Girija,S.V.S., and Rao,A.V.D. (2016). The Semicircular Reflected Gamma Distribution. i-manager’s Journal on Mathematics, 5(1), 39-46. https://doi.org/10.26634/JMAT.5.1.4870

References

[1]. Byoung J.A and Hyoung M.K, (2008). “A New Family of Semicircular Models: The Semicircular Laplace Distributions”. Communications of the Korean Statistical Society, Vol.15 (5), pp.775-781.

[2]. Dattatreya Rao A.V., Girija S.V.S. and Phani, (2016). “Stereographic Logistic Model – Application to Noisy Scrub Birds Data”. Chilean Journal of Statistics.

[3]. Dattatreya Rao A.V., Ramabhadra Sarma I. and Girija S.V.S, (2007). “On Wrapped Version of Some Life Testing Models”. Communication Statistics. - Theories and Methods, Vol.36(11), pp.2027-2035.

[4]. Dattatreya Rao A.V., Girija S.V.S. and Phani Y, (2011a). “On Stereographic Logistic Model”. Proceedings of NCAMES, pp.139 -141.

[5]. Dattatreya Rao A.V., Girija S.V.S. and Phani Y, (2011b). “Differential Approach to Cardioid Distribution”. Computer Engineering and Intelligent Systems, Vol.2(8), pp.1-6.

[6]. Dattatreya Rao A.V, S.V.S.Girija and A.J.V. Radhika, (2011c). “A Note on Offset Cauchy Distribution”. Proceedings of the 5 International Conference of IMBIC on Mathematical Sciences for Advancement of Science and Technology. pp.133-139.

[7]. Dattatreya Rao A.V, S.V.S. Girija, and V.J. Devaraaj, (2013a). “On the Rising Sun Wrapped Lognormal and the Rising Sun Wrapped Exponential Models”. International Journal of Statistics and Systems, Vol.3(1), pp.1-10.

[8]. Devaraaj V. J, (2012). “Some Contributions to Circular Statistics”. Unpublished PhD. Thesis, Acharya Nagarjuna University.

[9]. Devaraaj, S.V.S. Girija, and A.V.Dattatreya Rao, (2014). “Estimation of Parameters in Cardioid Distribution from Censored Samples”. International Journal Innovative Research in Science & Engineering (IJIRSE), pp.1-8.

[10]. Girija S.V.S, (2010). Construction of New Circular Models. Project number 36254, and ISBN 978-3-639-27939-9 VDM Verlag Dr. Müller GmbH & Co. KG.

[11]. Girija S.V.S, A.V. Dattatreya Rao, and Y. Phani, (2013a). “On Stereographic Lognormal Distribution”. International Journal of Advances in Applied Sciences (IJAAS), Vol.2(3), pp.125-132.

[12]. Girija S.V.S, A J V Radhika and A.V. Dattatreya Rao, (2013b). “On Bimodal Offset Cauchy Distribution”. Journal of the Applied Mathematics, Statistics and Informatics (JAMSI), Vol.9(1).

[13]. Girija S.V.S, A.J.V. Radhika and A.V.Dattatreya Rao, (2014a). “On Offset l-Arc Models”. Mathematics and Statistics, Vol.2(3), pp.127-136.

[14]. Girija S.V.S., A.V. Dattatreya Rao and Phani Yedlapalli, (2014b). “New Circular Model Induced by Inverse Stereographic projection on Double Exponential Model-Application to Birds Migration Data”. Journal of Applied Mathematics, Statistics and Informatics (JAMSI), Vol.10(1), pp.5-17.

[15]. Gradshteyn and Ryzhik, (2007). Table of Integrals, Series and Products. 7 edition, Academic Press.

[16]. Guardiola J.H, (2004). “The Semicircular Normal Distribution”. Ph.D. Dissertation, Institute of Statistics, Baylor University.

[17]. Jammalamadaka S. Rao and Sen Gupta A, (2001). Topics in Circular Statistics. World Scientific Press, Singapore.

[18]. Jones T.A, (1968). “Statistical Analysis of Orientation Data”. Journal of Sedimentary Petrology, Vol.38, pp.61-67.

[19]. Mardia K.V and Jupp P.E, (2000). Directional Statistics. John Wiley, Chichester.

[20]. Phani Y, Radhika A.J.V, Girija S.V.S. and Dattatreya Rao A.V, (2012b). “Modeling Ants Data Using Stereographic Reflected Gamma Distribution”. ANU Journal of Physical Science, Vol.4(1), pp.15-38.

[21]. Phani Y, S.V.S Girijaand A.V and Dattatreya Rao, (2012a). “Circular Model Induced by Inverse Stereographic Projection on Extreme-Value Distribution”. International Journal on Engineering Science and Technology, Vol.2(5), pp.881-888.

[22]. Phani Y, (2013). “On Stereographic Circular and Semicircular Models”. Unpublished PhD. Thesis, Acharya Nagarjuna University.

[23]. Phani Yedlapalli, Girija S.V.S., and Dattatreya Rao A.V., (2013a). “On Construction of Stereographic Semi Circular Models”. Journal of Applied Probability and Statistics, Vol.8(1), pp.75-90.

[24]. Phani Yedlapalli, A.J.V. Radhika, S.V.S. Girija and A.V. Dattatreya Rao, (2014). “New Circular Models induced by Modified Inverse Stereographic Projection on Arc Tan Exponential – Type Distribution”. International Journal of Mathematical Archive, Vol.5(4), pp.1-6.

[25]. Phani Y, Girija, S.V.S. and Dattatreya Rao A.V, (2015a). “ l -Axial Wrapped Exponential Distribution”. International Journal of Scientific and Innovative Mathematical Research (IJSIMR) , Special Issue, Vol.3(2), pp.463-467.

[26]. Phani Y., V. Sastry, Girija, S.V.S. and Dattatreya Rao A.V, (2015b). “A Note on Trigonometric Moments of Stereographic Circular / Semicircular Generalized Gamma Model”. International Journal of Advanced Research in Computer Science and Software Engineering (IJARCSSE), Vol.5(5).

[27]. Phani, Y, V. Sastry, S.V.S.Girija and A.V. Dattatreya Rao, (2015c). “A Note on Trigonometric moments of Marshall – Olkin Stereographic Circular Logistic Distribution”. International Research Journal of Engineering and Technology (IRJET), Vol.2(3).

[28]. Phani Yedlapalli, R.V. Babu, S.V.S.Girija and A.V.D. Rao, (2015d). “Stereographic –l-axial Exponential and Stereographic Circular Exponential Distribution”. International Journal of Scientific and Innovative Mathematical Research (IJSIMR). Special Issue, Vol.3(5), pp.108-114.

[29]. Radhika A.J.V, S.V.S.Girija and A.V. Dattatreya Rao, (2013a). “On Univariate Offset Pearson Type II Model – Application To Live Data”. International Journal of Mathematics and Statistics Studies, Vol.1(1), pp.1-9.

[30]. Radhika A.J.V, S.V.S. Girija and A.V. Dattatreya Rao, (2103b). “On Rising Sun von Mises and Rising Sun Wrapped Cauchy Circular Models”. Journal of the Applied Mathematics, Statistics and Informatics (JAMSI), Vol.9(2), pp.61- 67.

[31]. Radhika A.J.V, (2014). “Mathematical Tools in the Construction of New Circular Models”. Unpublished PhD. Thesis, Acharya Nagarjuna University,

[32]. Radhika A.J.V, S.V.S. Girija, and A.V. Dattatreya Rao, (2015). “On Characteristics of the Arc Offset Pareto Model”. International Journal Scientific and Innovative Mathematical Research (IJSIMR), Vol.3, pp.858-862.

[33]. Ugai. S.K., Nishijima, M. and Kan T, (1977). “Characteristics of Raindrop Size and Raindrop Shape”. Open Symposium URSI Commission, pp.225-230.

If you have access to this article please login to view the article or kindly login to purchase the article

Single Article

	North Americas,UK, Middle East,Europe		India	Rest of world
	USD	EUR	INR	USD-ROW
Online	15	15

ADD TO CART

Options for accessing this content:

If you would like institutional access to this content, please recommend the title to your librarian.
If you already have i-manager's user account: Login above and proceed to purchase the article.
New Users: Please register, then proceed to purchase the article.