Published

2013-01-01

The Family of Log-Skew-Normal Alpha-Power Distributions using Precipitation Data

La familia de distribuciones alfa-potencia log-skew-normal usando datos de precipitación

Keywords:

symmetry, Fisher information matrix, Kurtosis, Likelihood ratio test, Maximum likelihood estimator. (en)
Asimetría, curtosis, estimador máxima verosimilitud, matriz de información de Fisher, test de razón de verosimilitud. (es)

Authors

  • Guillermo Martínez-Flórez Universidad de Córdoba. Departamento de Matemáticas y Estadística
  • Sandra Vergara-Cardozo Universidad Nacional de Colombia. Facultad de Ciencias. Departamento de Estadística
  • Luz Mery González Universidad Nacional de Colombia. Facultad de Ciencias. Departamento de Estadística
We present a new set of distributions for positive data based on a skewnormal alpha-power (PSN) model including a new parameter which in turn makes the log-skew-normal alpha-power (LPSN) model more flexible than both the log-normal (LN) model and log-skew-normal (LSN) model. The LPSN model contains the LN model and LSN model as special cases. Furthermore, it models positive data with asymmetry and kurtosis larger than the one permitted by the LN distribution. Precipitation data illustrates the usefulness of the LPSN model being less influenced by outliers.

Presentamos una nueva familia de distribuciones para datos positivos basada en el modelo skew-normal alpha-power (PSN), incluyendo un nuevo parámetro el cual hace el modelo log-skew-normal alpha-power (LPSN) más flexible que los modelos log-normal (LN) y log-skew-normal (LSN). El modelo LPSN contiene el modelo LN y el modelo LSN como casos particulares. Además, modela datos positivos con asimetría y curtosis más allá de lo permitido por la distribución LN. Datos de precipitación ilustran la utilidad del modelo LPSN siendo menos influenciado por outliers.

The Family of Log-Skew-Normal Alpha-Power Distributions using Precipitation Data

La familia de distribuciones alfa-potencia log-skew-normal usando datos de precipitación

GUILLERMO MARTÍNEZ-FLÓREZ1, SANDRA VERGARA-CARDOZO2, LUZ MERY GONZÁLEZ3

1Universidad de Córdoba, Departamento de Matemáticas y Estadística, Montería, Colombia. Professor. Email: gmartinez@correo.unicordoba.edu.co
2Univesidad Nacional de Colombia, Facultad de Ciencias, Departamento de Estadística, Bogotá D.C, Colombia. Assistant professor. Email: svergarac@unal.edu.co
3Univesidad Nacional de Colombia, Facultad de Ciencias, Departamento de Estadística, Bogotá D.C, Colombia. Assistant professor. Email: lgonzalezg@unal.edu.co


Abstract

We present a new set of distributions for positive data based on a skew-normal alpha-power (PSN) model including a new parameter which in turn makes the log-skew-normal alpha-power (LPSN) model more flexible than both the log-normal (LN) model and log-skew-normal (LSN) model. The LPSN model contains the LN model and LSN model as special cases. Furthermore, it models positive data with asymmetry and kurtosis larger than the one permitted by the LN distribution. Precipitation data illustrates the usefulness of the LPSN model being less influenced by outliers.

Key words: Asymmetry, Fisher information matrix, Kurtosis, Likelihood ratio test, Maximum likelihood estimator.


Resumen

Presentamos una nueva familia de distribuciones para datos positivos basada en el modelo skew-normal alpha-power (PSN), incluyendo un nuevo parámetro el cual hace el modelo log-skew-normal alpha-power (LPSN) más flexible que los modelos log-normal (LN) y log-skew-normal (LSN). El\linebreak modelo LPSN contiene el modelo LN y el modelo LSN como casos particulares. Además, modela datos positivos con asimetría y curtosis más allá de lo permitido por la distribución LN. Datos de precipitación ilustran la utilidad del modelo LPSN siendo menos influenciado por outliers.

Palabras clave: asimetría, curtosis, estimador máxima verosimilitud, matriz de información de Fisher, test de razón de verosimilitud.


Texto completo disponible en PDF


References

1. Arnold, B. C. & Beaver, R. (2002), 'Skewed multivariate models related to hidden truncation and/or selective reporting', Test 11(1), 37-39.

2. Azzalini, A. (1985), 'A class of distributions which includes the normal ones', Scandinavian Journal of Statistics 12(2), 171-178.

3. Chaibub-Neto, E. & Branco, M. (2003), Bayesian Reference Analysis for Binomial Calibration Problem, IME-USP.

4. Chiogna, M. (1998), 'Some results on the scalar skew-normal distribution', Journal Italian Statistical Society 1, 1-13.

5. DiCiccio, T. J. & Monti, A. C. (2004), 'Inferential aspects of the skew exponential power distribution', Journal of the American Statistical Association 99, 439-450.

6. Durrans, S. R. (1992), 'Distributions of fractional order statistics in hydrology', Water Resources Research, 1649-1655.

7. Gupta, D. & Gupta, R. C. (2008), 'Analyzing skewed data by power normal model', Test 17(1), 197-210.

8. Gupta, R. S. & Gupta, R. D. (2004), 'Generalized skew normal model', Test 13(2), 501-524.

9. IDEAM, (2006), Estudio Agroclimático del Departamento de Córdoba, Fondo Editorial Universidad de Córdoba.

10. Lin, G. D. & Stoyanov, J. (2009), 'The logarithmic skew-normal distributions are moment-indeterminate', Journal of Applied Probability 46(3), 909-916.

11. Martínez-Flórez, G. (2011), Extensões do modelo α-potêncial, Tese de Doutorado, Instituto de Matemática e Estatística, Universidade de São Paulo, São Paulo.

12. R Development Core Team, (2011), R: A Language and Environment for Statistical Computing, R Foundation for Statistical Computing, Vienna, Austria. ISBN 3-900051-07-0. *http://www.R-project.org

13. Rotnitzky, A., Cox, D. R., Bottai, M. & Robins, J. (2000), 'Likelihood-based inference with singular information matrix', Bernoulli 6(2), 243-284.


[Recibido en junio de 2012. Aceptado en abril de 2013]

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

@ARTICLE{RCEv36n1a03,
    AUTHOR  = {Martínez-Flórez, Guillermo and Vergara-Cardozo, Sandra and González, Luz Mery},
    TITLE   = {{The Family of Log-Skew-Normal Alpha-Power Distributions using Precipitation Data}},
    JOURNAL = {Revista Colombiana de Estadística},
    YEAR    = {2013},
    volume  = {36},
    number  = {1},
    pages   = {43-57}
}

References

Akaike, H. (1974), ‘A new look at statistical model identification’, IEEE Transaction on Automatic Control (AU-19), 716–722.

Arnold, B. C. & Beaver, R. (2002), ‘Skewed multivariate models related to hidden truncation and/or selective reporting’.

Azzalini, A. (1985), ‘A class of distributions which includes the normal ones’, Scandinavian Journal of Statistics (12), 171–178.

Chaibub-Neto, E. & Branco, M. (2003), Bayesian Reference Analysis for Binomial Calibration Problem, IME-USP.

Chiogna, M. (1998), ‘Some results on the scalar skew-normal distribution’, Journal Italian Statistical Society 1, 1–13.

DiCiccio, T. J. & Monti, A. C. (2004), ‘Inferential aspects of the skew exponential power distribution’, Journal of the American Statistical Association 99, 439–450.

Durrans, S. R. (1992), ‘Distributions of fractional order statistics in hydrology’, Water Resources Research pp. 1649–1655.

Gupta, D. & Gupta, R. C. (2008), ‘Analyzing skewed data by power normal model’,Test 17(1), 197–210.

Gupta, R. S. & Gupta, R. D. (2004), ‘Generalized skew normal model’, Test 13(2), 501–524.

IDEAM (2006), Estudio Agroclimático del Departamento de Córdoba, Fondo Editorial Universidad de Córdoba.

Lin, G. D. & Stoyanov, J. (2009), ‘The logarithmic skew-normal distributions are moment-indeterminate’, Journal of Applied Probability 46(3), 909–916.

Martínez-Flórez, G. (2011), Extensões do modelo -potêncial, Tese de doutorado, Instituto de Matemática e Estatística, Universidade de São Paulo, São Paulo.

R Development Core Team (2011), R: A Language and Environment for Statistical Computing, R Foundation for Statistical Computing, Vienna, Austria. ISBN 3-900051-07-0.

*http://www.R-project.org

Rotnitzky, A., Cox, D. R., Bottai, M. & Robins, J. (2000), ‘Likelihood-based inference with singular information matrix’, Bernoulli 6(2), 243–284.

How to Cite

APA

Martínez-Flórez, G., Vergara-Cardozo, S. and González, L. M. (2013). The Family of Log-Skew-Normal Alpha-Power Distributions using Precipitation Data. Revista Colombiana de Estadística, 36(1), 43–57. https://revistas.unal.edu.co/index.php/estad/article/view/39583

ACM

[1]
Martínez-Flórez, G., Vergara-Cardozo, S. and González, L.M. 2013. The Family of Log-Skew-Normal Alpha-Power Distributions using Precipitation Data. Revista Colombiana de Estadística. 36, 1 (Jan. 2013), 43–57.

ACS

(1)
Martínez-Flórez, G.; Vergara-Cardozo, S.; González, L. M. The Family of Log-Skew-Normal Alpha-Power Distributions using Precipitation Data. Rev. colomb. estad. 2013, 36, 43-57.

ABNT

MARTÍNEZ-FLÓREZ, G.; VERGARA-CARDOZO, S.; GONZÁLEZ, L. M. The Family of Log-Skew-Normal Alpha-Power Distributions using Precipitation Data. Revista Colombiana de Estadística, [S. l.], v. 36, n. 1, p. 43–57, 2013. Disponível em: https://revistas.unal.edu.co/index.php/estad/article/view/39583. Acesso em: 29 mar. 2024.

Chicago

Martínez-Flórez, Guillermo, Sandra Vergara-Cardozo, and Luz Mery González. 2013. “The Family of Log-Skew-Normal Alpha-Power Distributions using Precipitation Data”. Revista Colombiana De Estadística 36 (1):43-57. https://revistas.unal.edu.co/index.php/estad/article/view/39583.

Harvard

Martínez-Flórez, G., Vergara-Cardozo, S. and González, L. M. (2013) “The Family of Log-Skew-Normal Alpha-Power Distributions using Precipitation Data”, Revista Colombiana de Estadística, 36(1), pp. 43–57. Available at: https://revistas.unal.edu.co/index.php/estad/article/view/39583 (Accessed: 29 March 2024).

IEEE

[1]
G. Martínez-Flórez, S. Vergara-Cardozo, and L. M. González, “The Family of Log-Skew-Normal Alpha-Power Distributions using Precipitation Data”, Rev. colomb. estad., vol. 36, no. 1, pp. 43–57, Jan. 2013.

MLA

Martínez-Flórez, G., S. Vergara-Cardozo, and L. M. González. “The Family of Log-Skew-Normal Alpha-Power Distributions using Precipitation Data”. Revista Colombiana de Estadística, vol. 36, no. 1, Jan. 2013, pp. 43-57, https://revistas.unal.edu.co/index.php/estad/article/view/39583.

Turabian

Martínez-Flórez, Guillermo, Sandra Vergara-Cardozo, and Luz Mery González. “The Family of Log-Skew-Normal Alpha-Power Distributions using Precipitation Data”. Revista Colombiana de Estadística 36, no. 1 (January 1, 2013): 43–57. Accessed March 29, 2024. https://revistas.unal.edu.co/index.php/estad/article/view/39583.

Vancouver

1.
Martínez-Flórez G, Vergara-Cardozo S, González LM. The Family of Log-Skew-Normal Alpha-Power Distributions using Precipitation Data. Rev. colomb. estad. [Internet]. 2013 Jan. 1 [cited 2024 Mar. 29];36(1):43-57. Available from: https://revistas.unal.edu.co/index.php/estad/article/view/39583

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