Published

2015-01-01

Slashed Rayleigh Distribution

Distribución Slashed Rayleigh

DOI:

https://doi.org/10.15446/rce.v38n1.48800

Keywords:

Kurtosis, Rayleigh Distribution, Slashed-elliptical Distributions, Slashed-Rayleigh Distribution, Slashed-Weibull Distribution, Weibull Distribution (en)
Curtosis, Distribución Rayleigh, Distribuciones Slashed-elípticas, Distribución Slashed-Rayleigh, Distribución Slashed-Weibull, DistribuciónWeibull. (es)

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Authors

  • Yuri A. Iriarte Universidad de Atacama - Instituto Tecnológico
  • Héctor W. Gómez Universidad de Antofagasta - Facultad de Ciencias Básicas - Departamento de Matemáticas
  • Héctor Varela Universidad de Antofagasta - Facultad de Ciencias Básicas - Departamento de Matemáticas
  • Heleno Bolfarine Universidade de São Paulo (USP) - Departamento de Estatística - Instituto de Matemática y Estatística

In this article we study a subfamily of the slashed-Weibull family. This subfamily can be seen as an extension of the Rayleigh distribution with more flexibility in terms of the kurtosis of distribution. This special feature makes the extension suitable for fitting atypical observations. It arises as the ratio of two independent random variables, the one in the numerator being a Rayleigh distribution and a power of the uniform distribution in the denominator. We study some probability properties, discuss maximum likelihood estimation and present real data applications indicating that the slashed-Rayleigh distribution can improve the ordinary Rayleigh distribution in fitting real data.

En este artículo estudiamos una subfamilia de la familia slashed-Weibull. Esta subfamilia puede ser vista como una extensión de la distribución Rayleigh con más flexibilidad en cuanto a la kurtosis de la distribución. Esta particularidad hace que la extensión sea adecuada para ajustar observaciones atípicas. Esto surge como la razón de dos variables aleatorias independientes, una en el numerador siendo una distribución Rayleigh y una potencia de la distribución uniforme en el denominador. Estudiamos algunas propiedades de probabilidad, discutimos la estimación de máxima verosimilitud y presentamos aplicaciones a datos reales indicando que la distribución slashed-Rayleigh presenta mejor ajuste para datos reales que la distribución Rayleigh.

https://doi.org/10.15446/rce.v38n1.48800

Slashed Rayleigh Distribution

Distribución Slashed Rayleigh

YURI A. IRIARTE1, HÉCTOR W. GÓMEZ2, HÉCTOR VARELA3, HELENO BOLFARINE4

1Universidad de Atacama, Instituto Tecnológico, Copiapó, Chile. Lecturer. Email: yuri.iriarte@uda.cl
2Universidad de Antofagasta, Facultad de Ciencias Básicas, Departamento de Matemáticas, Antofagasta, Chile. Professor. Email: hector.gomez@uantof.cl
3Universidad de Antofagasta, Facultad de Ciencias Básicas, Departamento de Matemáticas, Antofagasta, Chile. Professor. Email: hector.varela@uantof.cl
4Universidad de Sao Paulo, Instituto de Matemática y Estatística, Departamento de Estatística, Sao Paulo, Brasil. Professor. Email: hbolfar@ime.usp.br

Abstract

In this article we study a subfamily of the slashed-Weibull family. This subfamily can be seen as an extension of the Rayleigh distribution with more flexibility in terms of the kurtosis of distribution. This special feature makes the extension suitable for fitting atypical observations. It arises as the ratio of two independent random variables, the one in the numerator being a Rayleigh distribution and a power of the uniform distribution in the denominator. We study some probability properties, discuss maximum likelihood estimation and present real data applications indicating that the slashed-Rayleigh distribution can improve the ordinary Rayleigh distribution in fitting real data.

Key words: Kurtosis, RayleighDistribution, Slashed-elliptical Distributions, Slashed-Rayleigh Distribution, Slashed-Weibull Distribution, Weibull Distribution.

Resumen

En este artículo estudiamos una subfamilia de la familia slashed-Weibull. Esta subfamilia puede ser vista como una extensión de la distribución Rayleigh con más flexibilidad en cuanto a la kurtosis de la distribución. Esta particularidad hace que la extensión sea adecuada para ajustar observaciones atípicas. Esto surge como la razón de dos variables aleatorias independientes, una en el numerador siendo una distribución Rayleigh y una potencia de la distribución uniforme en el denominador. Estudiamos algunas propiedades de probabilidad, discutimos la estimación de máxima verosimilitud y presentamos aplicaciones a datos reales indicando que la distribución slashed-Rayleigh presenta mejor ajuste para datos reales que la distribución Rayleigh.

Palabras clave: curtosis, distribución Rayleigh, distribuciones Slashed-elípticas, distribución Slashed-Rayleigh, distribución Slashed-Weibull, distribución Weibull.

Texto completo disponible en PDF

References

1. Arslan, O. (2008), 'An alternative multivariate skew-slash distribution', Statistics and Probability Letters 78(16), 2756-2761.

2. Aubin, S. L. (1990), 'The lognormal distribution for modeling quality data when the mean is near zero', Journal of Quality Technology 22, 105-110.

3. Balakrishnan, N. & Kocherlakota, S. (1985), 'On the double Weibull distribution: order statistics and estimation', Sankhy\overline{a} 47, 161-178.

4. Cordeiro, G. M., Cristino, C. T., Hashimoto, E. M. & Ortega, E. M. (2013), 'The Beta generalized Rayleigh distribution with applications to lifetime data', Statistical Papers 54(1), 133-161.

5. Devore, J. (2005), Probabilidad y Estadística para Ingeniería y Ciencias, 6 edn, Editorial Thomson.

6. Fang, K. T., Kotz, S. & Ng, K. W. (1990), Symmetric Multivariate and Related Distributions, Chapman and Hall, New York.

7. Gómez, H. W., Olivares-Pacheco, J. F. & Bolfarine, H. (2009), 'An extension of the generalized Birnbaum-Saunders distribution', Statistics Probability Letters 79(3), 331-338.

8. Gómez, H. W., Quintana, F. A. & Torres, F. J. (2007), 'A new family of slash-distributions with elliptical contours', Statistics and Probability Letters 77(7), 717-725.

9. Gómez, H. W. & Venegas, O. (2008), 'Erratum to: a new family of slash-distributions with elliptical contours [statist. probab. lett. 77 (2007) 717-725]', Statistics Probability Letters 78(14), 2273-2274.

10. Gómez, Y. M., Bolfarine, H. & Gómez, H. W. (2014), 'A new extension of the exponential distribution', Revista Colombiana de Estadística 37, 25-34.

11. Johnson, N. L., Kotz, S. & Balakrishnan, N. (1994), Continuous Univariate Distributions, Vol. 1, 2 edn, Wiley, New York.

12. Kundu, D. & Raqab, M. Z. (2005), 'Generalized Rayleigh distribution: Different methods of estimation', Computational Statistics and Data Analysis 49, 187-200.

13. Manesh, S. F. & Khaledi, B. E. (2008), 'On the likelihood ratio order for convolutions of independent generalized Rayleigh random variables', Statistics and Probability Letters 78, 3139-3144.

14. Olivares-Pacheco, J. F., Cornide-Reyes, H. C. & Monasterio, M. (2010), 'An extension of the two-parameter Weibull distribution', Revista Colombiana de Estadística 33(2), 219-231.

15. Olmos, N. M., Varela, H., Gómez, H. W. & Bolfarine, H. (2012), 'An extension of the half-normal distribution', Statistical Papers 53, 875-886.

16. Surles, J. G. & Padgett, W. J. (2001), 'Inference for reliability and stress-strength for a scaled Burr type X distribution', Lifetime Data Analysis 7, 187-200.

17. Vod\checka, V. G. (1976), 'Inferential procedures on a generalized Rayleigh variate I', Applied Mathematics 21, 395-412.

[Recibido en septiembre de 2013. Aceptado en agosto de 2014]

Este artículo se puede citar en LaTeX utilizando la siguiente referencia bibliográfica de BibTeX:

@ARTICLE{RCEv38n1a02,
    AUTHOR  = {Iriarte, Yuri A. and Gómez, Héctor W. and Varela, Héctor and Bolfarine, Heleno},
    TITLE   = {{Slashed Rayleigh Distribution}},
    JOURNAL = {Revista Colombiana de Estadística},
    YEAR    = {2015},
    volume  = {38},
    number  = {1},
    pages   = {31-44}
}

References

Arslan, O. (2008), ‘An alternative multivariate skew-slash distribution’, Statistics and Probability Letters 78(16), 2756–2761.

Aubin, S. L. (1990), ‘The lognormal distribution for modeling quality data when the mean is near zero’, Journal of Quality Technology 22, 105–110.

Balakrishnan, N. & Kocherlakota, S. (1985), ‘On the double Weibull distribution: order statistics and estimation’, Sankhya 47, 161–178.

Cordeiro, G. M., Cristino, C. T., Hashimoto, E. M. & Ortega, E. M. (2013), ‘The Beta generalized Rayleigh distribution with applications to lifetime data’, Statistical Papers 54(1), 133–161.

Devore, J. (2005), Probabilidad y Estadística para Ingeniería y Ciencias, 6 edn, Editorial Thomson.

Fang, K. T., Kotz, S. & Ng, K. W. (1990), Symmetric Multivariate and Related Distributions, Chapman and Hall, New York.

Gómez, H. W., Olivares-Pacheco, J. F. & Bolfarine, H. (2009), ‘An extension of the generalized Birnbaum-Saunders distribution’, Statistics Probability Letters 79(3), 331–338.

Gómez, H. W., Quintana, F. A. & Torres, F. J. (2007), ‘A new family of slash-distributions with elliptical contours’, Statistics and Probability Letters 77(7), 717–725.

Gómez, H. W. & Venegas, O. (2008), ‘Erratum to: A new family of slashdistributions with elliptical contours [statist. probab. lett. 77 (2007) 717-725]’, Statistics Probability Letters 78(14), 2273–2274.

Gómez, Y. M., Bolfarine, H. & Gómez, H. W. (2014), ‘A new extension of the exponential distribution’, Revista Colombiana de Estadística 37, 25–34.

Johnson, N. L., Kotz, S. & Balakrishnan, N. (1994), Continuous Univariate Distributions, Vol. 1, 2 edn, Wiley, New York.

Kundu, D. & Raqab, M. Z. (2005), ‘Generalized Rayleigh distribution: Different methods of estimation’, Computational Statistics and Data Analysis 49, 187– 200.

Manesh, S. F. & Khaledi, B. E. (2008), ‘On the likelihood ratio order for convolutions of independent generalized Rayleigh random variables’, Statistics and Probability Letters 78, 3139–3144.

Olivares-Pacheco, J. F., Cornide-Reyes, H. C. & Monasterio, M. (2010), ‘An extensión of the two-parameter Weibull distribution’, Revista Colombiana de Estadística 33(2), 219–231.

Olmos, N. M., Varela, H., Gómez, H. W. & Bolfarine, H. (2012), ‘An extension of the half-normal distribution’, Statistical Papers 53, 875–886.

Surles, J. G. & Padgett, W. J. (2001), ‘Inference for reliability and stress-strength for a scaled Burr type x distribution’, Lifetime Data Analysis 7, 187–200.

Voda, V. G. (1976), ‘Inferential procedures on a generalized Rayleigh variate I’, Applied Mathematics 21, 395–412.

How to Cite

APA

Iriarte, Y. A., Gómez, H. W., Varela, H. and Bolfarine, H. (2015). Slashed Rayleigh Distribution. Revista Colombiana de Estadística, 38(1), 31–44. https://doi.org/10.15446/rce.v38n1.48800

ACM

[1]
Iriarte, Y.A., Gómez, H.W., Varela, H. and Bolfarine, H. 2015. Slashed Rayleigh Distribution. Revista Colombiana de Estadística. 38, 1 (Jan. 2015), 31–44. DOI:https://doi.org/10.15446/rce.v38n1.48800.

ACS

(1)
Iriarte, Y. A.; Gómez, H. W.; Varela, H.; Bolfarine, H. Slashed Rayleigh Distribution. Rev. colomb. estad. 2015, 38, 31-44.

ABNT

IRIARTE, Y. A.; GÓMEZ, H. W.; VARELA, H.; BOLFARINE, H. Slashed Rayleigh Distribution. Revista Colombiana de Estadística, [S. l.], v. 38, n. 1, p. 31–44, 2015. DOI: 10.15446/rce.v38n1.48800. Disponível em: https://revistas.unal.edu.co/index.php/estad/article/view/48800. Acesso em: 29 jan. 2025.

Chicago

Iriarte, Yuri A., Héctor W. Gómez, Héctor Varela, and Heleno Bolfarine. 2015. “Slashed Rayleigh Distribution”. Revista Colombiana De Estadística 38 (1):31-44. https://doi.org/10.15446/rce.v38n1.48800.

Harvard

Iriarte, Y. A., Gómez, H. W., Varela, H. and Bolfarine, H. (2015) “Slashed Rayleigh Distribution”, Revista Colombiana de Estadística, 38(1), pp. 31–44. doi: 10.15446/rce.v38n1.48800.

IEEE

[1]
Y. A. Iriarte, H. W. Gómez, H. Varela, and H. Bolfarine, “Slashed Rayleigh Distribution”, Rev. colomb. estad., vol. 38, no. 1, pp. 31–44, Jan. 2015.

MLA

Iriarte, Y. A., H. W. Gómez, H. Varela, and H. Bolfarine. “Slashed Rayleigh Distribution”. Revista Colombiana de Estadística, vol. 38, no. 1, Jan. 2015, pp. 31-44, doi:10.15446/rce.v38n1.48800.

Turabian

Iriarte, Yuri A., Héctor W. Gómez, Héctor Varela, and Heleno Bolfarine. “Slashed Rayleigh Distribution”. Revista Colombiana de Estadística 38, no. 1 (January 1, 2015): 31–44. Accessed January 29, 2025. https://revistas.unal.edu.co/index.php/estad/article/view/48800.

Vancouver

1.
Iriarte YA, Gómez HW, Varela H, Bolfarine H. Slashed Rayleigh Distribution. Rev. colomb. estad. [Internet]. 2015 Jan. 1 [cited 2025 Jan. 29];38(1):31-44. Available from: https://revistas.unal.edu.co/index.php/estad/article/view/48800

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10. Jimmy Reyes, Mario A. Rojas, Osvaldo Venegas, Héctor W. Gómez. (2020). Nakagami Distribution with Heavy Tails and Applications to Mining Engineering Data. Journal of Statistical Theory and Practice, 14(4) https://doi.org/10.1007/s42519-020-00122-7.

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