Correo Electrónico
DNINFOA - SIA
Bibliotecas
Convocatorias
Identidad U.N.
Published
A Semi-Circular Generalized Lindley Distribution with Applications to Orientation of Feldspar Laths and Outwash Pebbles Data
Distribución semicircular generalizada de Lindley para la orientación de laths de feldespato y material de arrastre: desarrollo teórico y evaluación del ajuste
DOI:
https://doi.org/10.15446/esrj.v30n1.120722Keywords:
ISP, generalized Lindley distribution, characteristic function, feldspar laths, outwash pebbles (en)ISP, distribución de Lindley generalizada, función característica, laths de feldespato, guijarros de arrastre (es)
Downloads
The study of rocks and minerals is very common for researchers in the field of science. However, in the context of real-life, inmense amounts of data exist related to the orientation of rocks and minerals which are often measured in terms of angles wherein their range is defined in [0, π). Thus, to deal with such types of datasets, a new semi-circular probability distribution has been introduced in this research by using the method of inverse stereographic projection (ISP), named as the semi-circular generalized Lindley (SCGL) distribution. Characteristic function and fundamental properties of the newly developed distribution are also studied. Method of maximum likelihood estimation is used to estimate the values of the parameters and . The applicability of the proposed distribution is shown by modelling 60 angular observations of feldspar laths in basalt and the orientation of pebbles.
El estudio de las rocas y minerales es muy común entre los investigadores en el campo de las ciencias. Sin embargo, en la práctica, existe una gran cantidad de datos relacionados con la orientación de las rocas y minerales, que a menudo se miden en términos de ángulos cuyo rango se define en [0, π). Por lo tanto, para abordar este tipo de conjuntos de datos, en esta investigación se introduce una nueva distribución de probabilidad semicircular utilizando el método de proyección estereográfica inversa (ISP), denominada distribución semicircular generalizada de Lindley (SCGL). También se estudian la función característica y las propiedades fundamentales de la distribución recientemente desarrollada. Se utiliza el método de máxima verosimilitud para estimar los valores de los parámetros. La aplicabilidad de la distribución propuesta se demuestra mediante la modelización de 60 observaciones angulares de laths de feldespato en basalto y la orientación de material de arrastre.
References
Abuzaid, A.H. (2018). A half-circular distribution for modeling the posterior corneal curvature. Communications in Statistics-Theory and Methods, 47(13), 3118-3124.
Ahn, B.J., & Kim, H.M. (2008). A new family of semi-circular models: The semi-circular Laplace distributions. Communications of the Korean Statistical Society, 15(5), 775–781.
Al-Omari, A.I., Al-Khazaleh, A.M.H., & Alzoubi, L.M. (2017). Transmuted Janardan distribution: A generalization of Janardan distribution. Journal of Statistics Applications & Probability, 5(2), 1-11.
Arnold, B.C., & SenGupta, A. (2006). Probability distributions and statistical inference for axial data. Environmental and Ecological Statistics, 13, 271-285.
Awad, N.T., & Mohammed, S.F. (2024). On stereographic semi-circular three parameter Lindley distribution. International Journal of Engineering and Information Systems, 8(1), 84-91.
Bodhisuwan, W., & Aryuyuen, S. (2022). The Poisson-transmuted Janardan distribution for modelling count data. Trends in Sciences, 19(5), 2898.
Dzivor, N.D., Otoo, H., & Wiah, E.N. (2021). Exponentiated Janardan distribution: A modification of Janardan distribution and application to life time data. International Journal of Probability and Statistics, 10(1), 9-16.
Fisher, N.I. (1993). Statistical Analysis of Circular Data. Cambridge University Press, Cambridge.
Fisher, R. (1953). Dispersion on a Sphere. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 217(1130): 295–305.
Iftikhar, A., Ali, A., & Hanif, M. (2022). Half circular modified Burr-III distribution, application with different estimation methods. PLoS ONE, 17(5), e0261901.
Krumbein, W.C. (1939). Preferred orientation of pebbles in sedimentary deposits. The Journal of Geology, 47(7), 673-706.
Lindley, D.V. (1958). Fiducial distributions and Bayes’ theorem. Journal of the Royal Statistical Society: Series B (Methodological), 20(1), 102-107.
Mardia, K.V., & Jupp, P.E. (2000). Directional Statistics. John Wiley & Sons, M. Baffins Lane, Chichester.
Minh, D.L., & Farnum, N.R. (2003). Using bilinear transformations to induce probability distributions. Communications in Statistics-Theory and Methods, 32(1), 1-9.
Mohammed, H.J., & Mohammed, S.F. (2023). On stereographic semi-circular Shankar distribution: Properties and applications. International Journal of Engineering and Information Systems, 7(9), 53-60.
Radhika, A.J.V., Yedlapalli, P., Raju, C.P., Kishore, G.N.V., Sri Krishna, A., & Pradeep Kumar, R.L.N. (2024). On stereographic semi-circular erlang distribution with application. Proceedings on Engineering Sciences, 6(3), 1299-1308.
Rambli, A., Mohamed, I. B., Shimizu, K., & Khalidin, N. (2015). Outlier detection in a new half-circular distribution. The 22nd National Symposium on Mathematical Sciences (SKSM22), Selangor, Malaysia, November, 1682(1), 050018(1-5).
Semary, H.E., Alshad, K. B., Bengalath, J., & Alghamdi, S. M. (2025). Semicircular Maxwell-Boltzmann distribution: Application to posterior corneal curvature data. Journal of Radiation Research and Applied Sciences, 18(2), 101471.
Shanker, R., Sharma, S., Shanker, U., & Shanker, R. (2013). Janardan distribution and its application to waiting times data. Indian Journal of Applied Research, 3(8), 500-502.
Shanker, R., Sharma, S., Shanker, U., Shanker, R., & Leonida, T.A. (2014). The discrete poison-Janardan distribution with application. International Journal of Soft Computing and Engineering, 4(2), 31-33.
Shekari, M., Zamani, H., & Saber, M. M. (2019). The compound class of Janardan–power series distributions: properties and applications. Journal of Data Science, 17(2), 259-278.
Watamori, Y. (1996). Statistical inference of Langevin distribution for directional data. Hiroshima Mathematical Journal, 26(1): 25–74.
Watson, G. S. (1984). The theory of concentrated Langevin distributions. Journal of Multivariate Analysis, 14(1), 74–82.
Yedlapalli, P., Kishore, G. N. V., Boulila, W., Koubaa, A., & Mlaiki, N. (2023). Toward enhanced geological analysis: A novel approach based on transmuted semicircular distribution. Symmetry, 15(11), 2030.
Yedlapalli, P., Girija, S. V. S., & Rao, A. V. D. (2013). On construction of stereographic semicircular models. Journal of Applied Probability and Statistics, 8(1), 75-90.
Yedlapalli, P., Girija, S.V.S., Rao, A.V.D., & Sastry, K.L.N. (2020). A new family of semicircular and circular arc tan-exponential type distributions. Thai Journal of Mathematics, 18 (2), 775-781.
Yedlapalli, P., Radhika, A.J.V., Girija, S.V.S., & Rao, A.V.D. (2017). On trigonometric moments of the stereographic semi-circular gamma distribution. European Journal of Pure and Applied Mathematics, 10(5), 1124-1134.
Yedlapalli, P., Sastry, K., & Rao, A. (2019). On stereographic semi-circular Quasi Lindley distribution. Journal of New Results in Science, 8(1), 6 -13.
How to Cite
APA
ACM
ACS
ABNT
Chicago
Harvard
IEEE
MLA
Turabian
Vancouver
Download Citation
License
Copyright (c) 2026 Earth Sciences Research Journal
This work is licensed under a Creative Commons Attribution 4.0 International License.
Earth Sciences Research Journal holds a Creative Commons Attribution license.
You are free to:
Share — copy and redistribute the material in any medium or format
Adapt — remix, transform, and build upon the material for any purpose, even commercially.
The licensor cannot revoke these freedoms as long as you follow the license terms.
The Earth Sciences Research Journal is the copyright holder for these license attributes.
