NEW SEMICIRCULAR DISTRIBUTION WITH APPLICATION

Authors:

Phani Yedlapalli,G. N. V. Kishore,A. J. V. Radhika,V. J. Devaraaj,Basireddi Rambabu,K. Ravibabu,

DOI NO:

https://doi.org/10.26782/jmcms.2026.03.00007

Keywords:

Axial data,semicircular model,inverse stereographic projection,trigonometric moments,simulation.,

Abstract

This article introduces a new semicircular distribution known as the stereographic semicircular new Weibull-Pareto distribution. We explore its various properties and provide explicit expressions for trigonometric moments. We delve into its essential mathematical properties and execute a simulation study to estimate its parameter values. Furthermore, we showcase the suggested distribution's modeling capacity in the context of real-world phenomena. An illustrative example is conducted using an authentic data set within the geological domain.

Refference:

I. A.H. Abuzaid.(2018).A half circular distribution for modeling the posterior corneal curvature, Communications in Statistics – Theory and Methods. 47(11), 3118-3124. 10.1080/036109. 26.2017.134852.
II. A. Iftikhar, A. Ali, and H.Muhammad(2022).Half circular burr-III distribution, application with different estimation methods. PLoS ONE.17 (5),1-21. e0261901. 10.1371/journal.pone0261901.
III. A.V.D.Rao, S.V.S.Girija, and P.Yedlapalli.(2011). On Stereographic Logistic Model. Proceedings of NCAMES, AU Engineering College, and Visakhapatnam, 139-141.
IV. A.V. Dattatreya Rao., S.V.S. Girija, and Y.Phani.(2016).Stereographic logistic Model-Application to Ornithology.Chilean Journal of Statistics. 7 (2),69-79.
V. B. Jin Ahn., and H.Moon.Kim(2008). A New Family of Semicircular Models: The Semicircular Laplace Distributions. Communications of the Korean Statistical Society. 15,775-781. 10.5351/CKSS.2008.15.5.775.
VI. C. Chesneau, L. Tomy and M. Jose.(2021). Wrapped Modified Lindley Distribution, Journal of Statistics and Management Systems. 24 (5),1025–10.1080/09720510.2020.1796313.
VII. Fisher I.N.(1993).Statistical Analysis of Circular Data. Cambridge University, University Press, Cambridge.
VIII. Guardiola, J.H.(2004). The Semicircular Normal Distribution. Ph.D. Dissertation, Baylor University, Institute of Statistics.
IX. H.Al-Mofleh, and S.Sen.(2019).The wrapped xgamma distribution for modeling circular data appearing in geological context, arXiv:1903.00177v1 [stat.ME]. 10.48550/arXiv.1903.00177.
X. J.H. Guardiola.( 2004). The Semicircular Normal Distribution. Ph.D. Dissertation, Baylor University,Institute of Statistics.
XI. K.V. Mardia and P.E. Jupp,.(2000). Directional Statistics, John Wiley, Chichester. 10.1002/9780470316979.
XII. Jones,T.A., (1968).Statistical Analysis of Orientation data, Journal of Sedimentary Petrology,38,61-67.
XIII. Minh and Farnum, Nicholas R.(2006). Using bilinear transformations to induce probability distributions. Communications in Statistics-Theory and Methods, 32 (1),1-9. 10.1081/STA-120017796.
XV. N.A. Oleiwi, S.H. Abid and N.H. Al-N.(2022). Transformed Semicircular Exponentiated Weibull Distribution, 3rd International Conference on Mathematics and Applied Science (ICMAS 2022) Journalof Physics: Conference Series. 1–17. 10.1088/1742-6596/2322/1/012036.
XVI. S.R.Jammalamadaka and A.Sengupta(2001). Topics in Circular Statistics, World Scientific Publishing, Singapore. https://doi.org/10.1142/4031.
XVII. S.R.Jammalamadaka, and T.Kozubowski.(2007). New families of wrapped distributions for modeling skew circular data. Communications in Statistics-Theory and Methods, 33(9),2059-2074. 10.1081/STA-200026570.
XVIII. S.Joshi, S. and K.K.Jose.(2018). Wrapped Lindley distribution. Communications in Statistics-Theory and Methods.47(5),1013-1021. 10.1080/03610926.2017.1280168.

XIX. Salah, H.A., H. Al-N, Nadia and A.E. Najm.(2023). Two doubly truncated semicircular distribution:Some important properties, Mustansiriyah Journal of Pure and Applied Sciences. 1 (1),164–174. 10.47831/mjpas.v1i1.18.
XX. P. Yedlapalli, S.V.S. Girija, and Dattatreya Rao A.V.(2013).On construction of semicircular models.Journal of Applied Probability and Statistics. 8 (1),75-90.
XXI. P. Yedlapalli. (2013a).On Stereographic Circular and Semicircular. Ph.D. Dissertation, Acharya Nagarjuna University.
XXII. P. Yedlapalli, S.V.S. Girija, A.V.D. Rao, and Sastry, K.L.N.( 2020).A new family of semicircular and Circular Arc tan-exponential type distribution.Thai Journal of Mathematics. 18(2),775-781.
XXIII. P. Rafael D. Marinho, Rodrigo B. Silva, Marcelo Bourguignon, Gauss M. Cordeiro, and N.Saralees. Adequacy Model: An R package for probability distributions and general purpose optimization. PLoS ONE, 14(8),(2019),1-30. 10.1371/journal.pone.0221487.
XXVI. Rao, A.V.D., I.R.Sharma, and S.V.S.Girija.(2007) .On Wrapped version of some life testing models. Communications in Statistics: Theory and Methods. 36 (11),2027-2035-1021. https://doi.org/10.1080/03610920601143832.
XXV. Rambli, A., Mohamed, I.B., Shimizu, K., and Khalidin N.(2015). Outlier detection in a new half-circular distribution. AIP Conference Proceedings, Selangor, Malaysia, 1-5.doi:10.1063/1.4932509.
XXVI. S. V. S. Girija, A.V.D. Rao, and Phani Y.(2013).On Stereographic lognormal Distribution. International Journal of Advances in Applied Sciences,2 (3),125-132. 10.11591/ijaas.v2.i3.pp125-132.
XXVII. Suleman N., Albert L.(2015).The new Weibull-Pareto distribution.Pak. Stat. oper.res. 11(1),103-114. 10.18187/pjsor.v11i1.863.
XXVIII.S. Bhattacharjee, I. Ahmed, and D.KishoreKumar.(2021). Wrapped Two-parameter Lindley distribution for modelling circular data. Thailand Statistician.19(1),81-94.
XXIX. Ugai, S., Kato, K., Nishijima, M. and Kan, T. (1977).Characteristics of raindrop size and raindrop shape. Open Symposium URSI Commission F.,,225-230.

View Download