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A new family of slash-distributions with elliptical contours

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  • Gómez, Héctor W.
  • Quintana, Fernando A.
  • Torres, Francisco J.

Abstract

We introduce a new family of univariate and multivariate slash-distributions. Our construction is based on elliptical distributions. We define the new family by means of a stochastic representation as the scale mixture of an elliptically distributed random variable with respect to the power of a U(0,1) random variable. The same idea is extended to the multivariate case. We study general properties of the resulting families, including their moments. We illustrate special cases of interest, such as Normal, Cauchy, Student-t, Type II Pearson and Kotz-type distributions.

Suggested Citation

  • Gómez, Héctor W. & Quintana, Fernando A. & Torres, Francisco J., 2007. "A new family of slash-distributions with elliptical contours," Statistics & Probability Letters, Elsevier, vol. 77(7), pages 717-725, April.
    • Handle: RePEc:eee:stapro:v:77:y:2007:i:7:p:717-725
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    References listed on IDEAS

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    1. Ashis Sengupta & Chandranath Pal, 2001. "On optimal tests for isotropy against the symmetric wrapped stable-circular uniform mixture family," Journal of Applied Statistics, Taylor & Francis Journals, vol. 28(1), pages 129-143.
    2. Cambanis, Stamatis & Huang, Steel & Simons, Gordon, 1981. "On the theory of elliptically contoured distributions," Journal of Multivariate Analysis, Elsevier, vol. 11(3), pages 368-385, September.
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    Cited by:

    1. Alcantara, Izabel Cristina & Cysneiros, Francisco José A., 2013. "Linear regression models with slash-elliptical errors," Computational Statistics & Data Analysis, Elsevier, vol. 64(C), pages 153-164.
    2. Neveka Olmos & Héctor Varela & Heleno Bolfarine & Héctor Gómez, 2014. "An extension of the generalized half-normal distribution," Statistical Papers, Springer, vol. 55(4), pages 967-981, November.
    3. Francisco A. Segovia & Yolanda M. Gómez & Osvaldo Venegas & Héctor W. Gómez, 2020. "A Power Maxwell Distribution with Heavy Tails and Applications," Mathematics, MDPI, vol. 8(7), pages 1-20, July.
    4. Bulut, Y. Murat & Arslan, Olcay, 2015. "Matrix variate slash distribution," Journal of Multivariate Analysis, Elsevier, vol. 137(C), pages 173-178.
    5. Jaime S. Castillo & Inmaculada Barranco-Chamorro & Osvaldo Venegas & Héctor W. Gómez, 2023. "Slash-Weighted Lindley Distribution: Properties, Inference, and Applications," Mathematics, MDPI, vol. 11(18), pages 1-14, September.
    6. Marjan Mansourian & Anoshirvan Kazemnejad & Iraj Kazemi & Farid Zayeri & Masoud Soheilian, 2012. "Bayesian analysis of longitudinal ordered data with flexible random effects using McMC: application to diabetic macular Edema data," Journal of Applied Statistics, Taylor & Francis Journals, vol. 39(5), pages 1087-1100, November.
    7. Pilar A. Rivera & Diego I. Gallardo & Osvaldo Venegas & Marcelo Bourguignon & Héctor W. Gómez, 2021. "An Extension of the Truncated-Exponential Skew- Normal Distribution," Mathematics, MDPI, vol. 9(16), pages 1-11, August.
    8. Talha Arslan, 2021. "An α -Monotone Generalized Log-Moyal Distribution with Applications to Environmental Data," Mathematics, MDPI, vol. 9(12), pages 1-18, June.
    9. Ali Genç, 2013. "A skew extension of the slash distribution via beta-normal distribution," Statistical Papers, Springer, vol. 54(2), pages 427-442, May.
    10. Jimmy Reyes & Yuri A. Iriarte, 2023. "A New Family of Modified Slash Distributions with Applications," Mathematics, MDPI, vol. 11(13), pages 1-15, July.
    11. Lachos, Victor H. & Castro, Luis M. & Dey, Dipak K., 2013. "Bayesian inference in nonlinear mixed-effects models using normal independent distributions," Computational Statistics & Data Analysis, Elsevier, vol. 64(C), pages 237-252.
    12. Jimmy Reyes & Yuri A. Iriarte & Pedro Jodrá & Héctor W. Gómez, 2019. "The Slash Lindley-Weibull Distribution," Methodology and Computing in Applied Probability, Springer, vol. 21(1), pages 235-251, March.
    13. Gómez, Yolanda M. & Bolfarine, Heleno & Gómez, Héctor W., 2019. "Gumbel distribution with heavy tails and applications to environmental data," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 157(C), pages 115-129.
    14. Neveka Olmos & Héctor Varela & Héctor Gómez & Heleno Bolfarine, 2012. "An extension of the half-normal distribution," Statistical Papers, Springer, vol. 53(4), pages 875-886, November.
    15. Arslan, Olcay, 2009. "Maximum likelihood parameter estimation for the multivariate skew-slash distribution," Statistics & Probability Letters, Elsevier, vol. 79(20), pages 2158-2165, October.
    16. del Castillo, J.M., 2016. "Slash distributions of the sum of independent logistic random variables," Statistics & Probability Letters, Elsevier, vol. 110(C), pages 111-118.
    17. Wenhao Gui, 2014. "A generalization of the slashed distribution via alpha skew normal distribution," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 23(4), pages 547-563, November.
    18. Arslan, Olcay, 2008. "An alternative multivariate skew-slash distribution," Statistics & Probability Letters, Elsevier, vol. 78(16), pages 2756-2761, November.
    19. Mario A. Rojas & Yuri A. Iriarte, 2022. "A Lindley-Type Distribution for Modeling High-Kurtosis Data," Mathematics, MDPI, vol. 10(13), pages 1-19, June.
    20. Gómez, Héctor W. & Olivares-Pacheco, Juan F. & Bolfarine, Heleno, 2009. "An extension of the generalized Birnbaum-Saunders distribution," Statistics & Probability Letters, Elsevier, vol. 79(3), pages 331-338, February.
    21. Maume-Deschamps, V. & Rullière, D. & Usseglio-Carleve, A., 2017. "Quantile predictions for elliptical random fields," Journal of Multivariate Analysis, Elsevier, vol. 159(C), pages 1-17.
    22. Karol I. Santoro & Diego I. Gallardo & Osvaldo Venegas & Isaac E. Cortés & Héctor W. Gómez, 2023. "A Heavy-Tailed Distribution Based on the Lomax–Rayleigh Distribution with Applications to Medical Data," Mathematics, MDPI, vol. 11(22), pages 1-15, November.
    23. V. Maume-Deschamps & D. Rullière & A. Usseglio-Carleve, 2018. "Spatial Expectile Predictions for Elliptical Random Fields," Methodology and Computing in Applied Probability, Springer, vol. 20(2), pages 643-671, June.

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