An extension of the slash-elliptical distribution

• Autores: Mario A. Rojas, Heleno Bolfarine, Hector W. Gómez
• Localización: Sort: Statistics and Operations Research Transactions, ISSN 1696-2281, Vol. 38, Nº. 2, 2014, págs. 215-230
• Idioma: inglés
• Enlaces
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• Resumen

  • This paper introduces an extension of the slash-elliptical distribution. This new distribution is generated as the quotient between two independent random variables, one from the elliptical family (numerator) and the other (denominator) a beta distribution. The resulting slash-elliptical distribution potentially has a larger kurtosis coefficient than the ordinary slash-elliptical distribution. We investigate properties of this distribution such as moments and closed expressions for the density function. Moreover, an extension is proposed for the location scale situation. Likelihood equations are derived for this more general version. Results of a real data application reveal that the proposed model performs well, so that it is a viable alternative to replace models with lesser kurtosis flexibility. We also propose a multivariate extension.

• Referencias bibliográficas
  • Akaike (1974). A new look at the statistical model identification. IEEE Transactions on Automatic Control, 19(6), 716–723.
  • Arellano-Valle, R. B., Bolfarine, H. and Vilca-Labra, F. (1996). Elliptical ultrastructural models. Canadian Journal of Statistics, 24(2),...
  • Arslan, O. (2008). An alternative multivariate skew-slash distribution. Statistics and Probability Letters, 78(16), 2756–2761.
  • Arslan, O. and Genc, A. I. (2009). A generalization of the multivariate slash distribution. Journal of Statistical Planning and Inference,...
  • Batschelet, E. (1981). Circular Statistics in Biology. London: Academic Press.
  • Byrd, R. H., Lu, P., Nocedal, J. and Zhu, C. (1995). A limited memory algorithm for bound constrained optimization. SIAM Journal on Scientific...
  • Fang, K. T., Kotz, S. and Ng, K. W. (1990). Symmetric Multivariate and Related Distributions. LondonNew York: Chapman and Hall.
  • Genc, A. I. (2007). A generalization of the univariate slash by a scale-mixture exponential power distribution. Communications in Statistics-Simulation...
  • Genc, A. I. (2013). A skew extension of the slash distribution via beta-normal distribution. Statistical Papers, 54(2), 427–442.
  • Gómez, H. W., Olivares-Pacheco, J. F. and Bolfarine, H. (2009). An extension of the generalized BirnbaumSaunders distribution. Statistics...
  • Gómez, H. W., Quintana, F. A. and Torres, F. J. (2007). New family of slash-distributions with elliptical contours. Statistics and Probability...
  • Gómez, H. W. and Venegas, O. (2008). Erratum to: a new family of slash-distributions with elliptical contours. Statistics and Probability...
  • Jander, R. (1957). Die optische richtungsorientierung der roten waldameise (Formica rufa L.). Zeitschrift für Vergleichende Physiologie,...
  • Jones, M. C. and Pewsey, A. (2004). A family of symmetric distributions on the circle. Technical Report, The Open University, Department of...
  • Johnson, N. L., Kotz, S. and Balakrishnan, N. (1995). Continuous Univariate Distributions, vol. 1, 2nd ed. New York: Wiley.
  • Kafadar, K. (1982). A biweight approach to the one-sample problem. Journal of the American Statistical Association, 77, 416–424.
  • Mosteller, F. and Tukey, J. W. (1977). Data Analysis and Regression. Addison-Wesley, Reading, MA.
  • Rogers, W. H. and Tukey, J. W. (1972). Understanding some long-tailed symmetrical distributions. Statistica Neerlandica, 26, 211–226.
  • SenGupta, A. and Pal, C. (2001). On optimal tests for isotropy against the symmetric wrapped stablecircular uniform mixture family. Journal...