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The location-scale mixture exponential power distribution: a Bayesian and maximum likelihood approach. (English) Zbl 1322.62077
Summary: We introduce an alternative skew-slash distribution by using the scale mixture of the exponential power distribution. We derive the properties of this distribution and estimate its parameter by maximum likelihood and Bayesian methods. By a simulation study we compute the mentioned estimators and their mean square errors, and we provide an example on real data to demonstrate the modeling strength of the new distribution.
MSC:
62E15 Exact distribution theory in statistics
60E05 Probability distributions: general theory
62F10 Point estimation
62F15 Bayesian inference
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[1] G. E. P. Box and G. C. Tiao, Bayesian Inference in Statistical Analysis, Addison-Wesley, Reading, Mass, USA, 1973. · Zbl 0341.62072
[2] R. A. Haro-López and A. F. M. Smith, “On robust Bayesian analysis for location and scale parameters,” Journal of Multivariate Analysis, vol. 70, no. 1, pp. 30-56, 1999. · Zbl 0962.62023 · doi:10.1006/jmva.1999.1820
[3] G. Agrò, “Maximum likelihood estimation for the exponential power function parameters,” Communications in Statistics. Simulation and Computation, vol. 24, no. 2, pp. 523-536, 1995. · Zbl 0850.62242 · doi:10.1080/03610919508813255
[4] T. J. DiCiccio and A. C. Monti, “Inferential aspects of the skew exponential power distribution,” The Journal of the American Statistical Association, vol. 99, no. 466, pp. 439-450, 2004. · Zbl 1117.62318 · doi:10.1198/016214504000000359 · puck.asa.catchword.org
[5] H. S. Salinas, R. B. Arellano-Valle, and H. W. Gómez, “The extended skew-exponential power distribution and its derivation,” Communications in Statistics. Theory and Methods, vol. 36, no. 9-12, pp. 1673-1689, 2007. · Zbl 1125.60010 · doi:10.1080/03610920601126118
[6] A. \DI. Gen\cc, “A generalization of the univariate slash by a scale-mixtured exponential power distribution,” Communications in Statistics. Simulation and Computation, vol. 36, no. 4-6, pp. 937-947, 2007. · Zbl 1126.62006 · doi:10.1080/03610910701539161
[7] D. Zhu and V. Zinde-Walsh, “Properties and estimation of asymmetric exponential power distribution,” Journal of Econometrics, vol. 148, no. 1, pp. 86-99, 2009. · Zbl 1429.62062 · doi:10.1016/j.jeconom.2008.09.038
[8] M. A. Hill and W. J. Dixon, “Robustness in real life: a study of clinical laboratory data,” Biometrics, vol. 38, no. 2, pp. 377-396, 1982. · doi:10.2307/2530452
[9] A. Azzalini, “Further results on a class of distributions which includes the normal ones,” Statistica, vol. 46, no. 2, pp. 199-208, 1986. · Zbl 0606.62013
[10] A. Azzalini, “A class of distributions which includes the normal ones,” Scandinavian Journal of Statistics, vol. 12, no. 2, pp. 171-178, 1985. · Zbl 0581.62014
[11] C. da Silva Ferreira, H. Bolfarine, and V. H. Lachos, “Skew scale mixtures of normal distributions: properties and estimation,” Statistical Methodology, vol. 8, no. 2, pp. 154-171, 2011. · Zbl 1213.62023 · doi:10.1016/j.stamet.2010.09.001
[12] K. E. Basford, D. R. Greenway, G. J. Mclachlan, and D. Peel, “Standard errors of fitted component means of normal mixtures,” Computational Statistics, vol. 12, pp. 1-17, 1997. · Zbl 0924.62055
[13] T. I. Lin, J. C. Lee, and S. Y. Yen, “Finite mixture modelling using the skew normal distribution,” Statistica Sinica, vol. 17, no. 3, pp. 909-927, 2007. · Zbl 1133.62012
[14] R. D. Cook, “Detection of influential observation in linear regression,” Technometrics, vol. 19, no. 1, pp. 15-18, 1977. · Zbl 0371.62096 · doi:10.2307/1268249
[15] A. Azzalini and A. Dalla Valle, “The multivariate skew-normal distribution,” Biometrika, vol. 83, no. 4, pp. 715-726, 1996. · Zbl 0885.62062 · doi:10.1093/biomet/83.4.715 · www3.oup.co.uk
[16] A. Azzalini and A. Capitanio, “Distributions generated by perturbation of symmetry with emphasis on a multivariate skew t-distribution,” Journal of the Royal Statistical Society B, vol. 65, no. 2, pp. 367-389, 2003. · Zbl 1065.62094 · doi:10.1111/1467-9868.00391
[17] M.G. Genton, Skew-Elliptical Distributions and Their Applications: A Journey Beyond Normality, Chapman and Hall/CRC, Boca Raton, Fla, USA, 2004. · Zbl 1069.62045 · doi:10.1201/9780203492000
[18] J. Wang and M. G. Genton, “The multivariate skew-slash distribution,” Journal of Statistical Planning and Inference, vol. 136, no. 1, pp. 209-220, 2006. · Zbl 1081.60013 · doi:10.1016/j.jspi.2004.06.023
[19] O. Arslan, “An alternative multivariate skew-slash distribution,” Statistics & Probability Letters, vol. 78, no. 16, pp. 2756-2761, 2008. · Zbl 1154.62336 · doi:10.1016/j.spl.2008.03.017
[20] H. Akaike, “A new look at the statistical model identification,” IEEE Transactions on Automatic Control, vol. 19, no. 6, pp. 716-723, 1974. · Zbl 0314.62039 · doi:10.1109/TAC.1974.1100705
[21] Z. D. Bai, P. R. Krishnaiah, and L. C. Zhao, “On rates of convergence of efficient detection criteria in signal processing with white noise,” IEEE Transactions on Information Theory, vol. 35, no. 2, pp. 380-388, 1989. · Zbl 0677.94001 · doi:10.1109/18.32132
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