THE BALAKRISHNAN-ALPHA-SKEW-NORMAL DISTRIBUTION: PROPERTIES AND APPLICATIONS BASN
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Published:
Jun 30, 2020
Keywords:
Skew Normal Distributions Alpha Skew Normal Distribution Balakrishnan Skew Normal Distributions Bimodal Distributions
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Abstract
In this paper a new type of alpha skew distribution is proposed under Balakrishnan (2002) Mechanism and some of its related distributions are investigated. The moments and distributional properties and some extensions related to this distribution are also studied. Suitability of the proposed distribution is tested by conducting data fitting experiments and model adequacy is checked via AIC and BIC in comparison with some related distributions. Likelihood ratio test is carried out to discriminate between normal and proposed distribution.
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Hazarika, P. J., Shah, S., & Chakraborty, S. (2020). THE BALAKRISHNAN-ALPHA-SKEW-NORMAL DISTRIBUTION: PROPERTIES AND APPLICATIONS: BASN. Malaysian Journal of Science, 39(2), 71–91. https://doi.org/10.22452/mjs.vol39no2.5
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Licensee MJS, Universiti Malaya, Malaysia. This article is an open-access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).
References
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Azzalini, A. (1985). A class of distributions which includes the normal ones. Scandinavian Journal of Statistics, 12(2), 171-185.
Bahrami, W., Agahi, H., and Rangin, H. (2009).A two-parameter Balakrishnan skew-normal distribution. J. Statist. Res. Iran 6: 231–242.
Balakrishnan, N. (2002). Discussion on “Skew multivariate models related to hidden truncation and/or selective reporting†by B. C. Arnold and R. J. Beaver. Test, 11:37-39
Chakraborty, S. and Hazarika, P.J. (2011). A survey of the theoretical developments in univariate skew normal distributions. Assam Statistical Review, 25(1), 41-63.
Chakraborty, S., Hazarika, P. J., and Ali, M. M. (2015). A multimodal skewed extension of normal distribution: its properties and applications. Statistics, 49(4), 859-877.
Cook, R. D., and Weisberg, S. (1994). An Introduction to Regression Graphics. New York: Wiley Series in Probability and Mathematical Statistics, John Wiley and Sons.
Elal-Olivero, D. (2010). Alpha-skew-normal distribution. Proyecciones (Antofagasta), 29(3), 224-240.
Harandi, S. S., and Alamatsaz, M. H. (2013). Alpha Skew Laplace distribution. Statistics and Probability Letters, 83(3), 774-782.
Hazarika, P. J., and Chakraborty, S. (2014). Alpha-Skew-Logistic Distribution. IOSR Journal of Mathematics, 10(4), 36-46.
Huang, W. J., and Chen, Y. H. (2007). Generalized skew- Cauchy distribution. Statistics and Probability Letters, 77(11), 1137-1147.
Louzada, F., Ara, A., and Fernandes, G. (2017). The bivariate alpha-skew-normal distribution. Communications in Statistics-Theory and Methods, 46(14), 7147-7156.
Nekoukhou, V., and Alamatsaz, M. H. (2012). A family of skew-symmetric-Laplace distributions. Statistical Papers, 53(3), 685-696.
Shafiei, S., Doostparast, M., and Jamalizadeh, A. (2016). The alpha–beta skew normal distribution: Properties and applications. Statistics, 50(2), 338-349.
Sharafi, M., and Behboodian, J. (2008). The Balakrishnan skew–normal density. Statistical Papers, 49(4), 769-778.
Sharafi, M., Sajjadnia, Z., and Behboodian, J. (2017). A new generalization of alpha-skew-normal distribution. Communications in Statistics-Theory and Methods, 46(12), 6098-6111.
Venegas, O., Bolfarine, H., Gallardo, D. I., Vergara-Fernández, A., and Gómez, H. W. (2016). A Note on the Log-Alpha-Skew-Normal Model with Geochemical Applications. Appl. Math, 10(5), 1697-1703.
Wahed, A., and Ali, M. M. (2001). The skew-logistic distribution. J. Statist. Res, 35(2), 71-80.
Xiang, Y., Gubian, S., Suomela, B., and Hoeng, J. (2013). Generalized Simulated Annealing for Global Optimization: The GenSA Package. R Journal, 5(1), 13-28.
Yadegari, I., Gerami, A., and Khaledi, M.J. (2008). A generalization of the Balakrishnan skew normal distribution. Stat. Probab. Lett. 78: 1165-1167.
Azzalini, A. (1985). A class of distributions which includes the normal ones. Scandinavian Journal of Statistics, 12(2), 171-185.
Bahrami, W., Agahi, H., and Rangin, H. (2009).A two-parameter Balakrishnan skew-normal distribution. J. Statist. Res. Iran 6: 231–242.
Balakrishnan, N. (2002). Discussion on “Skew multivariate models related to hidden truncation and/or selective reporting†by B. C. Arnold and R. J. Beaver. Test, 11:37-39
Chakraborty, S. and Hazarika, P.J. (2011). A survey of the theoretical developments in univariate skew normal distributions. Assam Statistical Review, 25(1), 41-63.
Chakraborty, S., Hazarika, P. J., and Ali, M. M. (2015). A multimodal skewed extension of normal distribution: its properties and applications. Statistics, 49(4), 859-877.
Cook, R. D., and Weisberg, S. (1994). An Introduction to Regression Graphics. New York: Wiley Series in Probability and Mathematical Statistics, John Wiley and Sons.
Elal-Olivero, D. (2010). Alpha-skew-normal distribution. Proyecciones (Antofagasta), 29(3), 224-240.
Harandi, S. S., and Alamatsaz, M. H. (2013). Alpha Skew Laplace distribution. Statistics and Probability Letters, 83(3), 774-782.
Hazarika, P. J., and Chakraborty, S. (2014). Alpha-Skew-Logistic Distribution. IOSR Journal of Mathematics, 10(4), 36-46.
Huang, W. J., and Chen, Y. H. (2007). Generalized skew- Cauchy distribution. Statistics and Probability Letters, 77(11), 1137-1147.
Louzada, F., Ara, A., and Fernandes, G. (2017). The bivariate alpha-skew-normal distribution. Communications in Statistics-Theory and Methods, 46(14), 7147-7156.
Nekoukhou, V., and Alamatsaz, M. H. (2012). A family of skew-symmetric-Laplace distributions. Statistical Papers, 53(3), 685-696.
Shafiei, S., Doostparast, M., and Jamalizadeh, A. (2016). The alpha–beta skew normal distribution: Properties and applications. Statistics, 50(2), 338-349.
Sharafi, M., and Behboodian, J. (2008). The Balakrishnan skew–normal density. Statistical Papers, 49(4), 769-778.
Sharafi, M., Sajjadnia, Z., and Behboodian, J. (2017). A new generalization of alpha-skew-normal distribution. Communications in Statistics-Theory and Methods, 46(12), 6098-6111.
Venegas, O., Bolfarine, H., Gallardo, D. I., Vergara-Fernández, A., and Gómez, H. W. (2016). A Note on the Log-Alpha-Skew-Normal Model with Geochemical Applications. Appl. Math, 10(5), 1697-1703.
Wahed, A., and Ali, M. M. (2001). The skew-logistic distribution. J. Statist. Res, 35(2), 71-80.
Xiang, Y., Gubian, S., Suomela, B., and Hoeng, J. (2013). Generalized Simulated Annealing for Global Optimization: The GenSA Package. R Journal, 5(1), 13-28.
Yadegari, I., Gerami, A., and Khaledi, M.J. (2008). A generalization of the Balakrishnan skew normal distribution. Stat. Probab. Lett. 78: 1165-1167.