References
- J.A. Baglivo, Mathematica Laboratories for Mathematical Statistics: Emphasizing Simulation and Computer Intensive Methods, Society for Industrial and Applied Mathematics, Pennsylvania, 2005.
- J.F. Bercher, A simple probabilistic construction yielding generalized entropies and divergences, escort distributions and q-Gaussians, Phys. A Stat. Mech. Appl. 391 (2012), pp. 4460–4469.
- J.F. Bercher, Some properties of generalized Fisher information in the context of nonextensive thermostatistics, Phys. A Stat. Mech. Appl. 392 (2013), pp. 3140–3154.
- M.N. Çankaya, Asymmetric bimodal exponential power distribution on the real line, Entropy 20 (2018), p. 23.
- M.N. Çankaya, M-estimations of shape and scale parameters by order statistics in least informative distributions on q-deformed logarithm, J. Inst. Sci. Technol. 10 (2020), pp. 1984–1996.
- M.N. Çankaya, Derivatives by ratio principle for q-sets on the time scale calculus, Fractals 29 (2021), p. 2140040. 10.1142/S0218348X21400405
- M.N. Çankaya and O. Arslan, On the robustness properties for maximum likelihood estimators of parameters in exponential power and generalized T distributions, Commun. Stat. Theory Methods 49 (2020), pp. 607–630.
- M.N. Çankaya and J. Korbel, Least informative distributions in maximum q-log-likelihood estimation, Physica A. 509 (2018), pp. 140–150.
- M.N. Çankaya, Y.M. Bulut, F.Z. Doğru, and O. Arslan, A bimodal extension of the generalized gamma distribution, Rev. Colomb. Estad. 38 (2015), pp. 371–384.
- M.N. Çankaya, A. Yalçınkaya, Ö. Altındağ, and O. Arslan, On the robustness of an epsilon skew extension for Burr III distribution on the real line, Comput. Stat. 34 (2019), pp. 1247–1273.
- F.Z. Doğru, Y.M. Bulut, and O. Arslan, Doubly reweighted estimators for the parameters of the multivariate t-distribution, Commun. Stat. Theory Methods 47 (2018), pp. 4751–4771.
- F. Domma, B.V. Popović, and S. Nadarajah, An extension of Azzalini's method, J. Comput. Appl. Math. 278 (2015), pp. 37–47.
- F. Domma, F. Condino, and B.V. Popović, A new generalized weighted Weibull distribution with decreasing, increasing, upside-down bathtub, N-shape and M-shape hazard rate, J. Appl. Stat. 44 (2017), pp. 2978–2993.
- R.C. Dunbar, Deriving the Maxwell distribution, J. Chem. Edu. 59 (1982), p. 22.
- D. Elal-Olivero, Alpha-skew-normal distribution, Proyecciones (Antofagasta) 29 (2010), pp. 224–240.
- B.S. Everitt and D.J. Hand, Finite Mixture Distributions, Springer Science & Business Media, New York, 2013.
- J.F. Feagin, Quantum Methods with Mathematica, Springer Science & Business Media, New York, 2002.
- D. Ferrari and Y. Yang, Maximum Lq-likelihood estimation, Ann. Stat. 38 (2010), pp. 753–783.
- R.A. Fisher, Theory of Statistical Estimation, Mathematical Proceedings of the Cambridge Philosophical Society, Vol. 22 (5), Cambridge University Press, 1925, pp. 700–725.
- E. Gómez-Déniz, J.M. Sarabia, and E. Calderín-Ojeda, Bimodal normal distribution: extensions and applications, J. Comput. Appl. Math. 388 (2021), pp. 113292.
- W. Härdle, M. Müller, S. Sperlich, and A. Werwatz, Nonparametric and Semiparametric Models (Vol. 1), Springer, Berlin, 2004.
- P.J. Huber, Robust estimation of a location parameter, Ann. Math. Stat. 35 (1964), pp. 73–101.
- S. Klugman, H. Panjer, and G. Willmot, Loss Models: From Data to Decisions, Wiley, New York, 1998.
- C. Lee, F. Famoye, and A.Y. Alzaatreh, Methods for generating families of univariate continuous distributions in the recent decades, Wiley Interdiscipl. Rev. Comput. Stat. 5 (2013), pp. 219–238.
- E.L. Lehmann and G. Casella, Theory of Point Estimation, Vol. 589, Wadsworth & Brooks/Cole, Pacific Grove, CA, 1998.
- J.G.S. León, Mathematica Beyond Mathematics: The Wolfram Language in the Real World, Chapman and Hall/CRC, Boca Raton, 2017.
- E.W. Ng and M. Geller, A table of integrals of the error functions, J. Res. Natl. Bur. Stand. Sec. B Math. Sci. 73B (1969), pp. 1–20.
- C.E.G. Otiniano, R. Vila, P.C. Brom, and M. Bourguignon, On the bimodal Gumbel model with application to environmental data, Aust. J. Stat. 52 (2023), pp. 45–65.
- A. Plastino, A.R. Plastino, and H.G. Miller, Tsallis nonextensive thermostatistics and Fisher's information measure, Physica A. 235 (1997), pp. 577–588.
- A.P. Prudnikov, I.U.A. Brychkov, and O.I. Marichev, Integrals and Series. Vol 2. Special Functions, Taylor & Francis, London, 2002.
- M. Rahman, B. Al-Zahrani, and M.Q. Shahbaz, Cubic transmuted Pareto distribution, Ann. Data Sci. 7 (2020), pp. 91–108.
- T.J. Rothenberg, Identification in parametric models, Econometrica 39 (1971), pp. 577–591.
- C.E. Shannon, A mathematical theory of communication, Bell Labs. Tech. J. 27 (1948), pp. 623–656.
- C. Tsallis, Possible generalization of Boltzmann–Gibbs statistics, J. Stat. Phys. 52 (1988), pp. 479–487.
- C. Tsallis, Introduction to Nonextensive Statistical Mechanics: Approaching a Complex World, Springer, New York, 2009.
- R. Vila and M.N. Çankaya, A bimodal Weibull distribution: properties and inference, J. Appl. Stat. 49 (2022), pp. 3044–3062.
- R. Vila, L. Ferreira, H. Saulo, F. Prataviera, and E.M.M. Ortega, A bimodal gamma distribution: properties, regression model and applications, Statistics 54 (2020), pp. 469–493.
- R. Vila, H. Saulo, and J. Roldan, On some properties of the bimodal normal distribution and its bivariate version, Chil. J. Stat. 12 (2021), pp. 125–144.
- R. Vila, L. Alfaia, A.F. Menezes, M.N. Çankaya, and M. Bourguignon, A model for bimodal rates and proportions, J. Appl. Stat. (2022), pp. 1–18. doi:10.1080/02664763.2022.2146661