Tan-G class of trigonometric distributions and its applications
- Luciano Souza lcnsza@gmail.com
- Wilson Rosa de O. Júnior wilson.rosa@gmail.com
- Cícero Carlos R. de Brito cicerocarlosbrito@yahoo.com.br
- Christophe Chesneau christophe.chesneau@unicaen.fr
- Renan L. Fernandes leandrorenanf@gmail.com
- Tiago A. E. Ferreira taef.first@gmail.com
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DOI:
https://doi.org/10.4067/S0719-06462021000100001Abstract
In this paper, we introduce a new general class of trigonometric distributions based on the tangent function, called the Tan-G class. A mathematical procedure of the Tan-G class is carried out, including expansions for the probability density function, moments, central moments and Rényi entropy. The estimates are acquired in a non-closed form by the maximum likelihood estimation method. Then, an emphasis is put on a particular member of this class defined with the Burr XII distribution as baseline, called the Tan-BXII distribution. The inferential properties of the Tan-BXII model are investigated. Finally, the Tan-BXII model is applied to a practical data set, illustrating the interest of the Tan-G class for the practitioner.
Keywords
T. W. Anderson and D. A. Darling, “A Test of Goodness-of-Fit”, Journal of the American Statistical Association, vol. 49, pp. 765–769, 1954.
C. C. R. Brito, “Método Gerador de Distribuiçoes e Classes de Distribuiçoes Probabilisticas”, Tese de doutorado (Doutorado em Biometria e Estatistica Aplicada), Universidade Federal Rural de Pernambuco, Recife, 2014.
G. Casella, and R. L. Berger, Statistical Inference, Brooks/Cole Publishing Company, California, 1990.
C. Chesneau, H. S. Bakouch, and T. Hussain, “A new class of probability distributions via cosine and sine functions with applications”, Communications in Statistics - Simulation and Computation, vol. 48, no. 8, pp. 2287–2300, 2019.
G. M. Cordeiro, and M. de Castro, “A new family of generalized distributions”, Journal of Statistical Computation and Simulation, vol. 81, no. 7, pp. 883–893, 2011.
A. Darling, “The Kolmogorov-Smirnov, Cramer-von Mises tests”, Annals of Mathematical Statistics, vol. 28, no 4, pp. 823–838, 1957.
R. D. Gupta, and D. Kundu, “Exponentiated exponential family: an alternative to gamma and Weibull distributions”, Biometrical Journal, vol. 43, no. 1, pp. 117–130, 2001.
F. Jamal, and C. Chesneau, “A new family of polyno-expo-trigonometric distributions with applications”, Infinite Dimensional Analysis, Quantum Probability and Related Topics, vol. 22, no. 04, 1950027, pp. 1–15, 2019.
S. Konishi, and G. Kitagawa, Information Criteria and Statistical Modeling. Springer, New York, 2007.
D. Kumar, U. Singh, and S. K. Singh, “A new distribution using sine function: its application to bladder cancer patients data”, Journal of Statistics Applications and Probability, vol. 4, no. 3, pp. 417–427, 2015.
Z. Mahmood, C. Chesneau, and M. H. Tahir, “A new sine-G family of distributions: properties and applications”, Bulletin of Computational Applied Mathematics, vol. 7, no. 1, pp. 53–81, 2019.
D. N. P. Murthy, M. Xie, and R. Jiag, Weibull Models, John Wiley and Sons, Inc. Hoboken, New Jersey, 2004.
A. Rényi, “On measures of entropy and information”, In: Proceedings of the 4th Berkeley Symposium on Mathematical Statistics and Probability, University of California Press, Berkeley, vol. 1, pp. 547–561, 1961.
R Development Core Team, R: A Language and Environment for Statistical Computing, R Foundation for Statistical Computing, Vienna, 2012.
C. E. Shannon, “Prediction and entropy of printed English”, The Bell System Technical Journal, vol. 30, no. 1, pp. 50–64, 1951.
L. Souza, “New trigonometric classes of probabilistic distributions”, Thesis, Universidade Federal Rural de Pernambuco, 2015.
L. Souza, L. Gallindo, and L. Serafim-de-Souza, (2016). TanB: The TanB Distribution. R package version 0.2. Available at https://cran.r-project.org/web/packages/TanB/ index.html or by running install.packages("TanB");library("TanB");help("rtanb") inside R([14]).
L. Souza, W. R. O. Junior, C. C. R. de Brito, C. Chesneau, T. A. E. Ferreira, and L. Soares, “On the Sin-G class of distributions: theory, model and application”, Journal of Mathematical Modeling, vol. 7, no. 3, pp. 357–379, 2019.
L. Souza, W. R. O. Junior, C. C. R. de Brito, C. Chesneau, T. A. E. Ferreira, and L. Soares, “General properties for the Cos-G class of distributions with applications”, Eurasian Bulletin of Mathematics, vol. 2, no. 2, pp. 63–79, 2019.
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